Ian & Stuart's Australian Mac 1993 September

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MacBinary | 1992-10-08 | 20.3 KB | [Ndc2/NCII]
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Win98 extracted |
DOS extracted
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This file was processed as: MacBinary (archive/macBinary).
Confidence	Program	Detection	Match Type	Support
`10%`	dexvert	MacBinary `(archive/macBinary)`	fallback	Supported
`100%`	file	MacBinary II, Fri Sep 4 17:24:27 1992, modified Thu Oct 8 10:00:55 1992, creator 'NCII', type 'Ndc2', 20182 bytes "Vectors and Matrices" , at 0x4f56 286 bytes resource	default (weak)
`99%`	file	data	default
`66%`	TrID	raw Group 3 FAX bitmap	default (weak)
`33%`	TrID	MacBinary 2	default (weak)
`100%`	siegfried	fmt/1762 MacBinary (II)	default
`100%`	lsar	MacBinary	default
id metadata
key	value
macFileType	`[Ndc2]`
macFileCreator	`[NCII]`
hex view
+--------+-------------------------+-------------------------+--------+--------+
|00000000| 00 14 56 65 63 74 6f 72 | 73 20 61 6e 64 20 4d 61 |..Vector|s and Ma|
|00000010| 74 72 69 63 65 73 00 00 | 00 00 00 00 00 00 00 00 |trices..|........|
|00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000040| 00 4e 64 63 32 4e 43 49 | 49 00 00 00 00 00 00 00 |.Ndc2NCI|I.......|
|00000050| 00 00 00 00 00 4e d6 00 | 00 01 1e a6 cd 84 8b a6 |.....N..|........|
|00000060| f9 ef 97 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 87 eb 00 00 |........|........|
|00000080| 51 59 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |QY......|........|
|00000090| 00 00 00 00 00 00 00 00 | 01 01 00 01 00 00 00 00 |........|........|
|000000a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000b0| 00 20 d7 44 00 20 d1 30 | 00 00 00 00 00 20 da 78 |. .D. .0|..... .x|
|000000c0| 00 20 cd e4 01 01 01 00 | 06 47 65 6e 65 76 61 98 |. ......|.Geneva.|
|000000d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000100| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000110| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000120| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000130| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000140| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000150| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000160| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000170| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000180| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000190| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000001a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000001b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000001c0| 00 00 00 00 00 00 00 00 | 00 09 00 00 01 3f 00 00 |........|.....?..|
|000001d0| 00 00 00 00 00 00 00 00 | 00 00 01 08 01 00 06 47 |........|.......G|
|000001e0| 65 6e 65 76 61 98 00 00 | 00 00 00 00 00 00 00 00 |eneva...|........|
|000001f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000200| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000210| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000220| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000230| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000240| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000250| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000260| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000270| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000280| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000290| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000002a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000002b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000002c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000002d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 09 |........|........|
|000002e0| 01 00 01 20 00 00 00 00 | 00 00 00 00 00 00 00 00 |... ....|........|
|000002f0| 00 00 00 07 00 00 40 0c | 9c 40 00 00 00 00 00 00 |......@.|.@......|
|00000300| 3f f1 d1 b7 17 58 e2 19 | 65 2c 00 05 00 00 40 08 |?....X..|e,....@.|
|00000310| fa 00 00 00 00 00 00 00 | 3f f5 83 12 6e 97 8d 4f |........|?...n..O|
|00000320| df 3b 00 07 00 00 40 0c | 9c 40 00 00 00 00 00 00 |.;....@.|.@......|
|00000330| 3f f1 d1 b7 17 58 e2 19 | 65 2c 00 02 00 00 40 08 |?....X..|e,....@.|
|00000340| fa 00 00 00 00 00 00 00 | 3f f5 83 12 6e 97 8d 4f |........|?...n..O|
|00000350| df 3b 00 04 00 00 40 08 | fa 00 00 00 00 00 00 00 |.;....@.|........|
|00000360| 3f f5 83 12 6e 97 8d 4f | df 3b 00 00 00 00 00 65 |?...n..O|.;.....e|
|00000370| 00 00 00 0a 00 0d 00 00 | 00 03 00 00 06 06 06 01 |........|........|
|00000380| 00 00 00 00 13 88 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000390| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000003a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000003b0| 00 07 02 6b 67 8a 00 20 | cd e8 00 00 02 fe 00 38 |...kg.. |.......8|
|000003c0| 55 1c 00 02 00 04 00 00 | 00 05 00 00 00 05 00 20 |U.......|....... |
|000003d0| d7 44 d7 44 00 38 01 6d | 67 8a 00 20 cd e8 00 00 |.D.D.8.m|g.. ....|
|000003e0| 02 fe 00 38 55 1c 00 02 | 00 04 00 00 00 05 00 00 |...8U...|........|
|000003f0| 00 05 00 20 d7 44 d7 44 | 00 38 03 73 65 63 00 20 |... .D.D|.8.sec. |
|00000400| cd e8 00 00 02 fe 00 38 | 55 1c 00 02 00 04 00 00 |.......8|U.......|
|00000410| 00 05 00 00 00 05 00 20 | d7 44 d7 44 00 38 04 64 |....... |.D.D.8.d|
|00000420| 65 67 4b 20 cd e8 00 00 | 02 fe 00 38 55 1c 00 02 |egK ....|...8U...|
|00000430| 00 04 00 00 00 05 00 00 | 00 05 00 20 d7 44 d7 44 |........|... .D.D|
|00000440| 00 38 04 63 6f 75 6c 20 | cd e8 00 00 02 fe 00 38 |.8.coul |.......8|
|00000450| 55 1c 00 02 00 04 00 00 | 00 05 00 00 00 05 00 20 |U.......|....... |
|00000460| d7 44 d7 44 00 38 04 6d | 6f 6c 65 20 cd e8 00 00 |.D.D.8.m|ole ....|
|00000470| 02 fe 00 38 55 1c 00 02 | 00 04 00 00 00 05 00 00 |...8U...|........|
|00000480| 00 05 00 20 d7 44 d7 44 | 00 38 07 64 6f 6c 6c 61 |... .D.D|.8.dolla|
|00000490| 72 73 00 00 02 fe 00 38 | 55 1c 00 02 00 04 00 00 |rs.....8|U.......|
|000004a0| 00 05 00 00 00 05 00 20 | d7 44 d7 44 00 38 00 00 |....... |.D.D.8..|
|000004b0| 00 00 07 00 20 da b8 00 | 00 00 00 00 00 00 00 00 |.... ...|........|
|000004c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000004d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 01 00 00 00 |........|........|
|000004e0| 03 00 20 da 8c 01 41 00 | 05 00 00 00 05 00 20 da |.. ...A.|...... .|
|000004f0| b8 00 38 4a 98 00 33 19 | cc 00 38 4a 84 00 00 00 |..8J..3.|..8J....|
|00000500| 04 00 00 00 05 00 20 cd | e8 00 00 00 1e 40 00 80 |...... .|.....@..|
|00000510| 00 00 00 00 00 00 00 40 | 00 c0 00 00 00 00 00 00 |.......@|........|
|00000520| 00 40 01 a0 00 00 00 00 | 00 00 00 0c 00 20 da 74 |.@......|..... .t|
|00000530| 01 00 00 00 00 00 00 00 | 00 00 00 00 00 00 17 00 |........|........|
|00000540| 00 00 00 00 04 61 63 6f | 73 00 00 20 00 20 3e 4c |.....aco|s.. . >L|
|00000550| 00 20 da 6c 00 00 00 1e | 00 38 4a 6e 00 35 48 5e |. .l....|.8Jn.5H^|
|00000560| 00 38 4a 5d 00 00 00 01 | 0f 00 20 d6 a4 00 00 00 |.8J]....|.. .....|
|00000570| 00 00 00 00 00 00 00 00 | 00 00 00 00 20 db 4c 00 |........|.... .L.|
|00000580| 00 00 00 00 20 d3 0c 00 | 20 cd e0 00 00 00 23 00 |.... ...| .....#.|
|00000590| 00 00 23 00 00 00 00 00 | 00 00 00 0c 41 6e 67 6c |..#.....|....Angl|
|000005a0| 65 42 65 74 77 65 65 6e | 20 db 4c 00 20 db 4c 00 |eBetween| .L. .L.|
|000005b0| 38 68 c8 00 38 4a 6c 40 | 80 9a 0a 00 20 cd e0 00 |8h..8Jl@|.... ...|
|000005c0| 00 00 23 20 20 61 63 6f | 73 28 56 a5 57 2f 28 20 |..#  aco|s(V.W/( |
|000005d0| 6c 65 6e 67 74 68 28 56 | 29 20 6c 65 6e 67 74 68 |length(V|) length|
|000005e0| 28 57 29 20 29 29 00 00 | 00 02 01 56 68 c8 00 38 |(W) ))..|...Vh..8|
|000005f0| 4a 5c 40 80 9a 0a 00 20 | cd e0 00 21 c5 14 00 38 |J\@.... |...!...8|
|00000600| a2 ff 00 00 ff ff 00 00 | 00 00 20 00 00 20 01 57 |........|.. .. .W|
|00000610| 68 c8 00 38 4a 5c 40 80 | 9a 0a 00 20 cd e0 00 21 |h..8J\@.|... ...!|
|00000620| c5 14 00 38 a2 ff 00 00 | ff ff 00 00 00 00 20 00 |...8....|...... .|
|00000630| 00 20 0c 00 20 d3 38 01 | 00 00 00 00 00 00 00 00 |. .. .8.|........|
|00000640| 00 00 00 00 00 15 00 00 | 00 00 00 03 61 72 67 20 |........|....arg |
|00000650| 00 00 20 00 00 00 02 00 | 20 db 4c 00 00 00 23 00 |.. .....| .L...#.|
|00000660| 38 4a 6e 00 35 48 5e 00 | 38 4a 5d 00 00 00 01 0c |8Jn.5H^.|8J].....|
|00000670| 00 20 d1 94 01 00 00 00 | 00 00 00 00 00 00 00 00 |. ......|........|
|00000680| 00 00 16 00 00 00 00 00 | 04 61 73 69 6e 00 00 20 |........|.asin.. |
|00000690| 00 00 00 02 00 20 db 4c | 00 00 00 23 00 38 4a 6e |..... .L|...#.8Jn|
|000006a0| 00 35 48 5e 00 38 4a 5d | 00 00 00 01 0c 00 20 da |.5H^.8J]|...... .|
|000006b0| bc 01 00 00 00 00 00 00 | 00 00 00 00 00 00 00 18 |........|........|
|000006c0| 00 00 00 00 00 04 61 74 | 61 6e 00 00 20 00 00 00 |......at|an.. ...|
|000006d0| 02 00 20 db 4c 00 00 00 | 23 00 38 4a 6e 00 35 48 |.. .L...|#.8Jn.5H|
|000006e0| 5e 00 38 4a 5d 00 00 00 | 01 09 00 20 db fc 00 00 |^.8J]...|... ....|
|000006f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 20 e0 10 |........|..... ..|
|00000700| 00 20 d1 ac 00 00 00 00 | 00 00 00 00 00 00 00 00 |. ......|........|
|00000710| 00 00 00 01 00 00 00 09 | 00 20 d1 58 01 42 cd e8 |........|. .X.B..|
|00000720| 00 00 00 01 00 38 4a 5d | 00 02 00 04 00 00 00 05 |.....8J]|........|
|00000730| 00 00 00 05 00 20 db fc | 00 00 ff ff 04 61 74 61 |..... ..|.....ata|
|00000740| 00 00 00 5a 40 01 a0 00 | 00 00 00 00 00 00 40 02 |...Z@...|......@.|
|00000750| b0 00 00 00 00 00 00 00 | 40 03 a8 00 00 00 00 00 |........|@.......|
|00000760| 00 00 40 02 80 00 00 00 | 00 00 00 00 40 02 e0 00 |..@.....|....@...|
|00000770| 00 00 00 00 00 00 40 03 | c0 00 00 00 00 00 00 00 |......@.|........|
|00000780| 40 02 b0 00 00 00 00 00 | 00 00 40 03 88 00 00 00 |@.......|..@.....|
|00000790| 00 00 00 00 40 03 d8 00 | 00 00 00 00 00 00 ff ff |....@...|........|
|000007a0| ff ff 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000007b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000007c0| 00 00 00 00 00 00 00 01 | 00 00 00 02 00 20 db bc |........|..... ..|
|000007d0| 00 00 00 14 40 00 c0 00 | 00 00 00 00 00 00 40 00 |....@...|......@.|
|000007e0| c0 00 00 00 00 00 00 00 | ff ff ff ff 00 00 00 00 |........|........|
|000007f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000800| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000810| 00 01 00 00 00 02 00 20 | cc f0 00 00 00 14 3f ff |....... |......?.|
|00000820| 80 00 00 00 00 00 00 00 | 3f ff 80 00 00 00 00 00 |........|?.......|
|00000830| 00 00 0e 00 20 d2 d4 01 | 00 00 00 00 00 00 00 00 |.... ...|........|
|00000840| 00 00 00 00 00 25 00 04 | 42 65 65 70 00 00 20 00 |.....%..|Beep.. .|
|00000850| 00 00 02 00 20 db 4c 00 | 00 00 23 00 38 4a 6e 00 |.... .L.|..#.8Jn.|
|00000860| 35 48 5e 00 38 4a 5d 00 | 00 00 01 04 00 20 d2 cc |5H^.8J].|..... ..|
|00000870| 01 00 00 00 00 00 00 00 | 00 00 00 00 00 00 38 00 |........|......8.|
|00000880| 05 42 65 67 69 6e 00 20 | 00 00 00 02 00 20 db 4c |.Begin. |..... .L|
|00000890| 00 00 00 23 00 38 4a 6e | 00 35 48 5e 00 38 4a 5d |...#.8Jn|.5H^.8J]|
|000008a0| 00 00 00 01 0c 00 20 d1 | 80 01 00 00 00 00 00 00 |...... .|........|
|000008b0| 00 00 00 00 00 00 00 11 | 00 00 00 00 00 03 63 6f |........|......co|
|000008c0| 73 69 6e 00 20 00 00 00 | 02 00 20 db 4c 00 00 00 |sin. ...|.. .L...|
|000008d0| 23 00 38 4a 6e 00 35 48 | 5e 00 38 4a 5d 00 00 00 |#.8Jn.5H|^.8J]...|
|000008e0| 01 12 00 20 ce f4 01 00 | 00 00 00 00 00 00 00 00 |... ....|........|
|000008f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000900| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 06 |........|........|
|00000910| 00 20 da a0 04 63 6f 75 | 6c 00 00 05 00 20 ce f4 |. ...cou|l.... ..|
|00000920| 00 20 e0 10 03 63 6f 73 | 69 6e 00 20 00 00 00 02 |. ...cos|in. ....|
|00000930| 00 20 db 4c 00 00 00 23 | 00 00 00 3c 3f ff 80 00 |. .L...#|...<?...|
|00000940| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000950| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000960| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 3f ff |........|......?.|
|00000970| 80 00 00 00 00 00 00 00 | 10 00 20 d2 a0 00 00 00 |........|.. .....|
|00000980| 00 00 00 00 00 00 00 00 | 00 00 00 00 20 d2 98 00 |........|.... ...|
|00000990| 00 00 00 00 20 d2 c8 00 | 20 d2 a8 00 a9 02 12 00 |.... ...| .......|
|000009a0| 00 02 1b 00 00 00 00 00 | 00 00 00 00 20 d2 78 36 |........|.... .x6|
|000009b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 07 43 72 |........|......Cr|
|000009c0| 6f 73 73 33 44 00 21 13 | 02 00 20 d2 98 00 20 d2 |oss3D.!.|.. ... .|
|000009d0| 98 00 38 68 c8 00 38 4a | 5c 40 80 9a 0a 00 20 d2 |..8h..8J|\@.... .|
|000009e0| a8 00 00 02 1b 66 75 6e | 63 74 69 6f 6e 20 43 72 |.....fun|ction Cr|
|000009f0| 6f 73 73 33 44 28 58 2c | 59 29 20 20 23 20 52 65 |oss3D(X,|Y)  # Re|
|00000a00| 74 75 72 6e 73 20 74 68 | 65 20 33 44 20 63 72 6f |turns th|e 3D cro|
|00000a10| 73 73 20 70 72 6f 64 75 | 63 74 20 6f 66 20 74 77 |ss produ|ct of tw|
|00000a20| 6f 20 33 44 20 76 65 63 | 74 6f 72 73 20 78 2c 79 |o 3D vec|tors x,y|
|00000a30| 2e 0d 2e 20 20 20 76 61 | 72 20 5a 0d 2e 20 20 20 |...   va|r Z..   |
|00000a40| 23 20 20 49 6e 70 75 74 | 3a 20 20 20 58 2c 59 5b |#  Input|:   X,Y[|
|00000a50| 31 c9 33 5d 20 33 2d 44 | 20 76 65 63 74 6f 72 73 |1.3] 3-D| vectors|
|00000a60| 0d 2e 20 20 20 23 20 20 | 4f 75 74 70 75 74 3a 20 |..   #  |Output: |
|00000a70| 43 72 6f 73 73 33 44 20 | 3d 20 58 20 63 72 6f 73 |Cross3D |= X cros|
|00000a80| 73 20 59 0d 2e 20 20 20 | 62 65 67 69 6e 0d 2e 20 |s Y..   |begin.. |
|00000a90| 20 20 20 20 20 69 66 20 | 73 69 7a 65 28 78 29 20 |     if |size(x) |
|00000aa0| 3c 3e 20 33 20 74 68 65 | 6e 0d 2e 20 20 20 20 20 |<> 3 the|n..     |
|00000ab0| 20 20 20 43 72 6f 73 73 | 33 44 20 3d 20 22 20 45 |   Cross|3D = " E|
|00000ac0| 52 52 4f 52 3a 20 58 20 | 6d 75 73 74 20 62 65 20 |RROR: X |must be |
|00000ad0| 61 20 33 44 20 76 65 63 | 74 6f 72 20 66 6f 72 20 |a 3D vec|tor for |
|00000ae0| 43 72 6f 73 73 33 44 22 | 0d 2e 20 20 20 20 20 20 |Cross3D"|..      |
|00000af0| 65 6c 73 65 20 69 66 20 | 73 69 7a 65 28 79 29 20 |else if |size(y) |
|00000b00| 3c 3e 20 33 20 74 68 65 | 6e 0d 2e 20 20 20 20 20 |<> 3 the|n..     |
|00000b10| 20 20 20 20 43 72 6f 73 | 73 33 44 20 3d 20 22 20 |    Cros|s3D = " |
|00000b20| 45 52 52 4f 52 3a 20 59 | 20 6d 75 73 74 20 62 65 |ERROR: Y| must be|
|00000b30| 20 61 20 33 44 20 76 65 | 63 74 6f 72 20 66 6f 72 | a 3D ve|ctor for|
|00000b40| 20 43 72 6f 73 73 33 44 | 22 0d 2e 20 20 20 20 20 | Cross3D|"..     |
|00000b50| 20 65 6c 73 65 0d 2e 20 | 20 20 20 20 20 62 65 67 | else.. |     beg|
|00000b60| 69 6e 0d 2e 20 20 20 20 | 20 20 20 20 7a 5b 31 5d |in..    |    z[1]|
|00000b70| 20 3d 20 78 5b 32 5d 20 | 79 5b 33 5d 20 2d 20 78 | = x[2] |y[3] - x|
|00000b80| 5b 33 5d 20 79 5b 32 5d | 3b 0d 2e 20 20 20 20 20 |[3] y[2]|;..     |
|00000b90| 20 20 20 7a 5b 32 5d 20 | 3d 20 78 5b 33 5d 20 79 |   z[2] |= x[3] y|
|00000ba0| 5b 31 5d 20 2d 20 78 5b | 31 5d 20 79 5b 33 5d 3b |[1] - x[|1] y[3];|
|00000bb0| 0d 2e 20 20 20 20 20 20 | 20 20 7a 5b 33 5d 20 3d |..      |  z[3] =|
|00000bc0| 20 78 5b 31 5d 20 79 5b | 32 5d 20 2d 20 78 5b 32 | x[1] y[|2] - x[2|
|00000bd0| 5d 20 79 5b 31 5d 3b 0d | 2e 20 20 20 20 20 20 20 |] y[1];.|.       |
|00000be0| 20 43 72 6f 73 73 33 44 | 20 3d 20 7a 0d 2e 20 20 | Cross3D| = z..  |
|00000bf0| 20 20 20 20 65 6e 64 0d | 2e 20 20 20 20 65 6e 64 |    end.|.    end|
|00000c00| 00 00 00 02 01 58 68 c8 | 00 38 4a 4c 40 80 9a 0a |.....Xh.|.8JL@...|
|00000c10| 00 20 d2 a8 00 21 c5 14 | 00 38 a2 ff 00 00 ff ff |. ...!..|.8......|
|00000c20| 00 00 00 00 20 00 00 20 | 01 59 68 c8 00 38 4a 4c |.... .. |.Yh..8JL|
|00000c30| 40 80 9a 0a 00 20 d2 a8 | 00 21 c5 14 00 38 a2 ff |@.... ..|.!...8..|
|00000c40| 00 00 ff ff 00 00 00 00 | 20 00 00 20 00 00 00 01 |........| .. ....|
|00000c50| 01 5a c5 14 00 38 a2 ff | 00 00 ff ff 00 00 00 00 |.Z...8..|........|
|00000c60| 20 00 00 20 00 00 00 02 | 00 20 d2 98 00 00 02 1b | .. ....|. ......|
|00000c70| 00 34 93 0c 12 00 20 d1 | 2c 01 00 00 00 00 00 00 |.4.... .|,.......|
|00000c80| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000c90| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000ca0| 00 00 05 00 20 d2 94 04 | 64 65 67 4b 00 00 05 00 |.... ...|degK....|
|00000cb0| 20 d1 2c 00 20 d2 98 00 | 00 02 1b 00 34 93 0c 00 | .,. ...|....4...|
|00000cc0| 00 00 01 00 00 ff ff 00 | 00 00 00 00 00 00 32 3f |........|......2?|
|00000cd0| ff 80 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000ce0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000cf0| 00 00 00 00 00 00 00 3f | ff 80 00 00 00 00 00 00 |.......?|........|
|00000d00| 00 0c 00 20 d1 28 01 00 | 00 00 00 00 00 00 00 00 |... .(..|........|
|00000d10| 00 00 00 00 22 00 00 00 | 00 00 06 44 65 6c 65 74 |...."...|...Delet|
|00000d20| 65 20 00 20 3e 4c 00 20 | d2 44 00 00 00 32 00 38 |e . >L. |.D...2.8|
|00000d30| 4a 6e 00 35 48 5e 00 38 | 4a 5d 00 00 00 01 0c 00 |Jn.5H^.8|J]......|
|00000d40| 20 d2 74 01 00 00 00 00 | 00 00 00 00 00 00 00 00 | .t.....|........|
|00000d50| 00 42 00 00 00 00 00 09 | 44 69 6d 65 6e 73 69 6f |.B......|Dimensio|
|00000d60| 6e 3e 4c 00 20 d2 44 00 | 00 00 32 00 38 4a 6e 00 |n>L. .D.|..2.8Jn.|
|00000d70| 35 48 5e 00 38 4a 5d 00 | 00 00 01 04 00 20 dc 1c |5H^.8J].|..... ..|
|00000d80| 01 00 00 00 00 00 00 00 | 00 00 00 00 00 00 3b 00 |........|......;.|
|00000d90| 02 44 6f 6d 65 6e 73 69 | 6f 6e 3e 4c 00 20 d2 44 |.Domensi|on>L. .D|
|00000da0| 00 00 00 32 00 38 4a 6e | 00 35 48 5e 00 38 4a 5d |...2.8Jn|.5H^.8J]|
|00000db0| 00 00 00 01 12 00 20 d3 | a8 01 00 00 00 00 00 00 |...... .|........|
|00000dc0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000dd0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000de0| 00 00 08 00 20 d3 b0 07 | 64 6f 6c 6c 61 72 73 00 |.... ...|dollars.|
|00000df0| 20 d3 a8 00 00 ff ff 02 | 44 6f 6d 65 6e 73 69 6f | .......|Domensio|
|00000e00| 6e 3e 4c 00 20 d2 44 00 | 00 00 32 00 00 00 50 3f |n>L. .D.|..2...P?|
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|00001d00| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001d10| 00 00 00 00 00 00 00 00 | 00 00 00 00 07 00 20 d4 |........|...... .|
|00001d20| 84 04 6d 6f 6c 65 00 00 | 05 00 20 d3 cc 00 00 ff |..mole..|.. .....|
|00001d30| ff 07 4d 69 6e 69 6d 75 | 6d 00 35 5d ce 00 35 5d |..Minimu|m.5]..5]|
|00001d40| ce 00 00 00 00 00 00 00 | 46 3f ff 80 00 00 00 00 |........|F?......|
|00001d50| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001d60| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001d70| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001d80| 00 00 00 00 00 3f ff 80 | 00 00 00 00 00 00 00 0c |.....?..|........|
|00001d90| 00 20 ce a0 01 00 00 00 | 00 00 00 00 00 00 00 00 |. ......|........|
|00001da0| 00 00 26 00 00 00 00 00 | 04 4e 61 6d 65 00 00 20 |..&.....|.Name.. |
|00001db0| 00 20 3e 4c 00 20 d4 14 | 00 00 00 46 00 38 4a 6e |. >L. ..|...F.8Jn|
|00001dc0| 00 35 48 5e 00 38 4a 5d | 00 00 00 01 0c 00 20 d2 |.5H^.8J]|...... .|
|00001dd0| 68 01 00 00 00 00 00 00 | 00 00 00 00 00 00 00 41 |h.......|.......A|
|00001de0| 00 00 00 00 00 05 50 72 | 69 6e 74 00 20 00 20 3e |......Pr|int. . >|
|00001df0| 4c 00 20 d4 14 00 00 00 | 46 00 38 4a 6e 00 35 48 |L. .....|F.8Jn.5H|
|00001e00| 5e 00 38 4a 5d 00 00 00 | 01 04 00 20 d3 94 01 00 |^.8J]...|... ....|
|00001e10| 00 00 00 00 00 00 00 00 | 00 00 00 00 35 00 09 50 |........|....5..P|
|00001e20| 72 6f 63 65 64 75 72 65 | 3e 4c 00 20 d4 14 00 00 |rocedure|>L. ....|
|00001e30| 00 46 00 38 4a 6e 00 35 | 48 5e 00 38 4a 5d 00 00 |.F.8Jn.5|H^.8J]..|
|00001e40| 00 01 0c 00 20 d3 58 01 | 00 00 00 00 00 00 00 00 |.... .X.|........|
|00001e50| 00 00 00 00 00 44 00 00 | 00 00 00 07 50 72 6f 64 |.....D..|....Prod|
|00001e60| 75 63 74 72 65 3e 4c 00 | 20 d4 14 00 00 00 46 00 |uctre>L.| .....F.|
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|00001e80| 00 20 ce 9c 01 00 00 00 | 00 00 00 00 00 00 00 00 |. ......|........|
|00001e90| 00 00 35 00 07 50 72 6f | 67 72 61 6d 72 65 3e 4c |..5..Pro|gramre>L|
|00001ea0| 00 20 d4 14 00 00 00 46 | 00 38 4a 6e 00 35 48 5e |. .....F|.8Jn.5H^|
|00001eb0| 00 38 4a 5d 00 00 00 01 | 0c 00 20 d2 0c 01 00 00 |.8J]....|.. .....|
|00001ec0| 00 00 00 00 00 00 00 00 | 00 00 00 1e 00 00 00 00 |........|........|
|00001ed0| 00 04 52 65 61 6c 72 61 | 6d 72 65 3e 4c 00 20 d4 |..Realra|mre>L. .|
|00001ee0| 14 00 00 00 46 00 38 4a | 6e 00 35 48 5e 00 38 4a |....F.8J|n.5H^.8J|
|00001ef0| 5d 00 00 00 01 12 00 20 | dc 14 01 00 00 00 00 00 |]...... |........|
|00001f00| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001f10| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001f20| 00 00 00 04 00 20 d7 50 | 03 73 65 63 00 00 00 05 |..... .P|.sec....|
|00001f30| 00 20 dc 14 00 00 ff ff | 04 52 65 61 6c 72 61 6d |. ......|.Realram|
|00001f40| 72 65 3e 4c 00 20 d4 14 | 00 00 00 46 00 00 00 28 |re>L. ..|...F...(|
|00001f50| 3f ff 80 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |?.......|........|
|00001f60| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 3f ff |........|......?.|
|00001f70| 80 00 00 00 00 00 00 00 | 0c 00 20 ce 8c 01 00 00 |........|.. .....|
|00001f80| 00 00 00 00 00 00 00 00 | 00 00 00 47 00 00 00 00 |........|...G....|
|00001f90| 00 04 53 69 67 6e 00 00 | 20 00 20 3e 4c 00 20 da |..Sign..| . >L. .|
|00001fa0| a4 00 00 00 28 00 38 4a | 6e 00 35 48 5e 00 38 4a |....(.8J|n.5H^.8J|
|00001fb0| 5d 00 00 00 01 0c 00 20 | ce 90 01 00 00 00 00 00 |]...... |........|
|00001fc0| 00 00 00 00 00 00 00 00 | 10 00 00 00 00 00 03 73 |........|.......s|
|00001fd0| 69 6e 6e 00 00 20 00 20 | 3e 4c 00 20 da a4 00 00 |inn.. . |>L. ....|
|00001fe0| 00 28 00 38 4a 6e 00 35 | 48 5e 00 38 4a 5d 00 00 |.(.8Jn.5|H^.8J]..|
|00001ff0| 00 01 0c 00 20 d2 ec 01 | 00 00 00 00 00 00 00 00 |.... ...|........|
|00002000| 00 00 00 00 00 1c 00 00 | 00 00 00 04 53 69 7a 65 |........|....Size|
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|00002030| 00 20 ce cc 01 00 00 00 | 00 00 00 00 00 00 00 00 |. ......|........|
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|00002060| 00 35 48 5e 00 38 4a 5d | 00 00 00 01 0c 00 20 ce |.5H^.8J]|...... .|
|00002070| 64 01 00 00 00 00 00 00 | 00 00 00 00 00 00 00 19 |d.......|........|
|00002080| 00 00 00 00 00 04 73 71 | 72 74 41 73 49 66 52 65 |......sq|rtAsIfRe|
|00002090| 61 6c 20 da a4 00 00 00 | 28 00 38 4a 6e 00 35 48 |al .....|(.8Jn.5H|
|000020a0| 5e 00 38 4a 5d 00 00 00 | 01 0c 00 20 da 50 01 00 |^.8J]...|... .P..|
|000020b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 1a 00 00 00 |........|........|
|000020c0| 00 00 03 53 75 6d 74 41 | 73 49 66 52 65 61 6c 20 |...SumtA|sIfReal |
|000020d0| da a4 00 00 00 28 00 38 | 4a 6e 00 35 48 5e 00 38 |.....(.8|Jn.5H^.8|
|000020e0| 4a 5d 00 00 00 01 0d 00 | 20 ce 68 01 00 00 00 00 |J]......| .h.....|
|000020f0| 00 00 00 00 00 00 00 00 | 00 46 00 00 00 00 00 00 |........|.F......|
|00002100| 00 00 00 00 00 ff ff 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002110| 00 05 54 61 62 6c 65 73 | 49 66 52 65 61 6c 20 da |..Tables|IfReal .|
|00002120| a4 00 00 00 28 00 38 4a | 6e 00 35 48 5e 00 38 4a |....(.8J|n.5H^.8J|
|00002130| 5d 00 00 00 01 0c 00 20 | ce 6c 01 00 00 00 00 00 |]...... |.l......|
|00002140| 00 00 00 00 00 00 00 00 | 12 00 00 00 00 00 03 74 |........|.......t|
|00002150| 61 6e 6c 65 73 49 66 52 | 65 61 6c 20 da a4 00 00 |anlesIfR|eal ....|
|00002160| 00 28 00 38 4a 6e 00 35 | 48 5e 00 38 4a 5d 00 00 |.(.8Jn.5|H^.8J]..|
|00002170| 00 01 04 00 20 e0 14 01 | 00 00 00 00 00 00 00 00 |.... ...|........|
|00002180| 00 00 00 00 00 3e 00 04 | 54 68 65 6e 65 73 49 66 |.....>..|ThenesIf|
|00002190| 52 65 61 6c 20 da a4 00 | 00 00 28 00 38 4a 6e 00 |Real ...|..(.8Jn.|
|000021a0| 35 48 5e 00 38 4a 5d 00 | 00 00 01 10 00 20 dd 64 |5H^.8J].|..... .d|
|000021b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 20 |........|....... |
|000021c0| d3 f8 00 00 00 00 00 20 | ce 3c 00 20 dd a4 00 6b |....... |.<. ...k|
|000021d0| 01 b2 00 00 01 b9 00 00 | 00 00 00 00 00 00 00 20 |........|....... |
|000021e0| ce 40 36 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |.@6.....|........|
|000021f0| 05 54 72 61 63 65 00 05 | 00 21 13 02 00 20 d3 f8 |.Trace..|.!... ..|
|00002200| 00 20 d3 f8 00 38 68 c8 | 00 38 4a 5c 40 80 9a 0a |. ...8h.|.8J\@...|
|00002210| 00 20 dd a4 00 00 01 b9 | 66 75 6e 63 74 69 6f 6e |. ......|function|
|00002220| 20 54 72 61 63 65 28 74 | 68 65 4d 61 74 72 69 78 | Trace(t|heMatrix|
|00002230| 29 20 23 20 52 65 74 75 | 72 6e 73 20 74 68 65 20 |) # Retu|rns the |
|00002240| 73 75 6d 20 6f 66 20 74 | 68 65 20 64 69 61 67 6f |sum of t|he diago|
|00002250| 6e 61 6c 20 65 6c 65 6d | 65 6e 74 73 20 6f 66 20 |nal elem|ents of |
|00002260| 61 20 6d 61 74 72 69 78 | 2e 0d 2e 20 20 76 61 72 |a matrix|...  var|
|00002270| 20 64 2c 41 6e 73 77 65 | 72 0d 2e 20 20 62 65 67 | d,Answe|r..  beg|
|00002280| 69 6e 0d 2e 20 20 20 20 | 20 20 64 20 3d 20 64 69 |in..    |  d = di|
|00002290| 6d 65 6e 73 69 6f 6e 28 | 74 68 65 4d 61 74 72 69 |mension(|theMatri|
|000022a0| 78 29 0d 2e 20 20 20 20 | 20 20 41 6e 73 77 65 72 |x)..    |  Answer|
|000022b0| 20 3d 20 30 0d 2e 20 20 | 20 20 20 20 69 66 20 73 | = 0..  |    if s|
|000022c0| 69 7a 65 28 64 29 3c 3e | 32 20 74 68 65 6e 20 0d |ize(d)<>|2 then .|
|000022d0| 2e 20 20 20 20 20 20 20 | 20 20 41 6e 73 77 65 72 |.       |  Answer|
|000022e0| 20 3d 20 22 20 45 52 52 | 4f 52 3a 20 61 72 67 75 | = " ERR|OR: argu|
|000022f0| 6d 65 6e 74 20 74 6f 20 | 54 72 61 63 65 20 6d 75 |ment to |Trace mu|
|00002300| 73 74 20 62 65 20 61 20 | 6d 61 74 72 69 78 2e 22 |st be a |matrix."|
|00002310| 0d 2e 20 20 20 20 20 20 | 65 6c 73 65 20 69 66 20 |..      |else if |
|00002320| 64 5b 31 5d 3c 3e 64 5b | 32 5d 20 74 68 65 6e 0d |d[1]<>d[|2] then.|
|00002330| 2e 20 20 20 20 20 20 20 | 20 20 20 41 6e 73 77 65 |.       |   Answe|
|00002340| 72 20 3d 20 22 20 45 52 | 52 4f 52 3a 20 6d 61 74 |r = " ER|ROR: mat|
|00002350| 72 69 78 20 66 6f 72 20 | 54 72 61 63 65 20 6d 75 |rix for |Trace mu|
|00002360| 73 74 20 62 65 20 73 71 | 75 61 72 65 2e 22 0d 2e |st be sq|uare."..|
|00002370| 20 20 20 20 20 20 65 6c | 73 65 0d 2e 20 20 20 20 |      el|se..    |
|00002380| 20 20 20 20 20 66 6f 72 | 20 6a 3d 31 c9 64 5b 31 |     for| j=1.d[1|
|00002390| 5d 20 64 6f 20 41 6e 73 | 77 65 72 20 3d 20 41 6e |] do Ans|wer = An|
|000023a0| 73 77 65 72 20 2b 20 74 | 68 65 4d 61 74 72 69 78 |swer + t|heMatrix|
|000023b0| 5b 6a 2c 6a 5d 0d 2e 20 | 20 20 20 20 54 72 61 63 |[j,j].. |    Trac|
|000023c0| 65 20 3d 20 41 6e 73 77 | 65 72 0d 2e 20 20 65 6e |e = Answ|er..  en|
|000023d0| 64 00 00 00 01 09 74 68 | 65 4d 61 74 72 69 78 9a |d.....th|eMatrix.|
|000023e0| 0a 00 20 dd a4 00 21 c5 | 14 00 38 a2 ff 00 00 ff |.. ...!.|..8.....|
|000023f0| ff 00 00 00 00 20 00 00 | 20 00 00 00 02 01 64 c5 |..... ..| .....d.|
|00002400| 14 00 38 a2 ff 00 00 ff | ff 00 00 00 00 20 00 00 |..8.....|..... ..|
|00002410| 20 00 00 00 01 00 20 d3 | f8 00 00 01 b9 00 34 93 | ..... .|......4.|
|00002420| 0c 06 41 6e 73 77 65 72 | ff 00 00 ff ff 00 00 00 |..Answer|........|
|00002430| 00 20 00 00 20 00 00 00 | 01 00 20 d3 f8 00 00 01 |. .. ...|.. .....|
|00002440| b9 00 34 93 0c 0c 00 20 | d1 24 01 00 00 00 00 00 |..4.... |.$......|
|00002450| 00 00 00 00 00 00 00 00 | 04 00 00 00 00 00 09 54 |........|.......T|
|00002460| 72 61 6e 73 70 6f 73 65 | 00 02 00 00 ff ff 00 00 |ranspose|........|
|00002470| 00 00 00 38 4a 6e 00 35 | 48 5e 00 38 4a 5d 00 00 |...8Jn.5|H^.8J]..|
|00002480| 00 01 0c 00 20 ce 38 01 | 00 00 00 00 00 00 00 00 |.... .8.|........|
|00002490| 00 00 00 00 00 21 00 00 | 00 00 00 06 55 6e 4c 6f |.....!..|....UnLo|
|000024a0| 63 6b 6f 73 65 00 02 00 | 00 ff ff 00 00 00 00 00 |ckose...|........|
|000024b0| 38 4a 6e 00 35 48 5e 00 | 38 4a 5d 00 00 00 01 04 |8Jn.5H^.|8J].....|
|000024c0| 00 20 ce 34 01 00 00 00 | 00 00 00 00 00 00 00 00 |. .4....|........|
|000024d0| 00 00 37 00 03 56 61 72 | 6f 63 6b 6f 73 65 00 02 |..7..Var|ockose..|
|000024e0| 00 00 ff ff 00 00 00 00 | 00 38 4a 6e 00 35 48 5e |........|.8Jn.5H^|
|000024f0| 00 38 4a 5d 00 00 00 01 | 04 00 20 d3 5c 01 00 00 |.8J]....|.. .\...|
|00002500| 00 00 00 00 00 00 00 00 | 00 00 00 40 00 05 57 68 |........|...@..Wh|
|00002510| 69 6c 65 6b 6f 73 65 00 | 02 00 00 ff ff 00 00 00 |ilekose.|........|
|00002520| 00 00 38 4a 6e 00 35 48 | 5e 00 38 4a 5d 00 00 00 |..8Jn.5H|^.8J]...|
|00002530| 01 05 00 20 d1 54 01 00 | 00 00 00 00 00 00 00 00 |... .T..|........|
|00002540| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002550| 00 00 00 00 00 00 06 78 | 43 6c 69 63 6b 6f 73 65 |.......x|Clickose|
|00002560| 00 02 ff 00 00 02 12 ae | 40 80 00 38 4a 6e 00 35 |........|@..8Jn.5|
|00002570| 48 5e 00 38 4a 5d 00 00 | 00 01 05 00 20 cd d8 01 |H^.8J]..|.... ...|
|00002580| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002590| 00 3f ff 80 00 00 00 00 | 00 00 00 00 00 00 00 04 |.?......|........|
|000025a0| 78 4d 61 78 63 6b 6f 73 | 65 00 02 ff 00 00 02 12 |xMaxckos|e.......|
|000025b0| ae 40 80 00 38 4a 6e 00 | 35 48 5e 00 38 4a 5d 00 |.@..8Jn.|5H^.8J].|
|000025c0| 00 00 01 05 00 20 d1 8c | 01 00 00 00 00 00 00 00 |..... ..|........|
|000025d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000025e0| 00 00 00 00 00 00 00 00 | 04 78 4d 69 6e 63 6b 6f |........|.xMincko|
|000025f0| 73 65 00 02 ff 00 00 02 | 12 ae 40 80 00 38 4a 6e |se......|..@..8Jn|
|00002600| 00 35 48 5e 00 38 4a 5d | 00 00 00 01 05 00 20 d3 |.5H^.8J]|...... .|
|00002610| a4 01 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002620| 00 00 00 3f fb cc cc cc | cc cc cc cc cd 00 00 00 |...?....|........|
|00002630| 00 04 78 50 69 78 63 6b | 6f 73 65 00 02 ff 00 00 |..xPixck|ose.....|
|00002640| 02 12 ae 40 80 00 38 4a | 6e 00 35 48 5e 00 38 4a |...@..8J|n.5H^.8J|
|00002650| 5d 00 00 00 01 05 00 20 | d4 10 01 00 00 00 00 00 |]...... |........|
|00002660| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002670| 00 00 00 00 00 00 00 00 | 00 00 06 79 43 6c 69 63 |........|...yClic|
|00002680| 6b 6f 73 65 00 02 ff 00 | 00 02 12 ae 40 80 00 38 |kose....|....@..8|
|00002690| 4a 6e 00 35 48 5e 00 38 | 4a 5d 00 00 00 01 05 00 |Jn.5H^.8|J]......|
|000026a0| 20 da ec 01 00 00 00 00 | 00 00 00 00 00 00 00 00 | .......|........|
|000026b0| 00 00 00 00 00 3f ff 80 | 00 00 00 00 00 00 00 00 |.....?..|........|
|000026c0| 00 00 00 04 79 4d 61 78 | 63 6b 6f 73 65 00 02 ff |....yMax|ckose...|
|000026d0| 00 00 02 12 ae 40 80 00 | 38 4a 6e 00 35 48 5e 00 |.....@..|8Jn.5H^.|
|000026e0| 38 4a 5d 00 00 00 01 05 | 00 20 d5 24 01 00 00 00 |8J].....|. .$....|
|000026f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002700| 00 00 00 00 00 00 00 00 | 00 00 00 00 04 79 4d 69 |........|.....yMi|
|00002710| 6e 63 40 80 9b 70 00 38 | 00 02 00 38 a2 5a 00 00 |nc@..p.8|...8.Z..|
|00002720| 00 38 4a 6e 00 35 48 5e | 00 38 4a 5d 00 00 00 01 |.8Jn.5H^|.8J]....|
|00002730| 05 00 20 d4 00 01 00 00 | 00 00 00 00 00 00 00 00 |.. .....|........|
|00002740| 00 00 00 00 00 00 00 3f | fb cc cc cc cc cc cc cc |.......?|........|
|00002750| cd 00 00 00 00 04 79 50 | 69 78 63 40 80 9b 70 00 |......yP|ixc@..p.|
|00002760| 38 00 02 00 38 a2 5a 00 | 00 00 38 4a 6e 00 35 48 |8...8.Z.|..8Jn.5H|
|00002770| 5e 00 38 4a 5d 00 00 00 | 01 00 00 00 00 00 00 00 |^.8J]...|........|
|00002780| 00 00 00 00 00 01 00 20 | da 84 00 00 00 00 00 00 |....... |........|
|00002790| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000027a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000027b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000027c0| 00 00 00 00 00 00 00 01 | 01 00 00 00 00 00 00 2a |........|.......*|
|000027d0| 00 0a 01 4c 01 9b 00 47 | 72 61 70 68 65 78 20 50 |...L...G|raphex P|
|000027e0| 6c 61 6e 65 00 00 00 00 | 00 00 00 00 00 00 00 00 |lane....|........|
|000027f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002800| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002810| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002820| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002830| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002840| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002850| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002860| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002870| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002880| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002890| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000028a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000028b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000028c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000028d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000028e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000028f0| 1a 42 56 65 63 74 6f 72 | 73 20 61 6e 64 20 4d 61 |.BVector|s and Ma|
|00002900| 74 72 69 63 65 73 0d 0d | 53 6f 6d 65 20 65 78 61 |trices..|Some exa|
|00002910| 6d 70 6c 65 73 20 6f 66 | 20 77 6f 72 6b 20 77 69 |mples of| work wi|
|00002920| 74 68 20 76 65 63 74 6f | 72 73 20 61 6e 64 20 6d |th vecto|rs and m|
|00002930| 61 74 72 69 63 65 73 2e | 20 20 46 6f 72 20 6d 61 |atrices.|  For ma|
|00002940| 74 72 69 78 20 69 6e 76 | 65 72 73 69 6f 6e 2c 20 |trix inv|ersion, |
|00002950| 65 69 67 65 6e 76 61 6c | 75 65 73 2c 20 61 6e 64 |eigenval|ues, and|
|00002960| 20 64 65 74 65 72 6d 69 | 6e 61 6e 74 2c 20 61 6e | determi|nant, an|
|00002970| 64 20 6f 74 68 65 72 20 | 6d 69 73 63 65 6c 6c 61 |d other |miscella|
|00002980| 6e 65 6f 75 73 20 6d 61 | 74 72 69 78 20 61 6e 64 |neous ma|trix and|
|00002990| 20 76 65 63 74 6f 72 20 | 66 75 6e 63 74 69 6f 6e | vector |function|
|000029a0| 73 2c 20 73 65 65 20 74 | 68 65 20 4c 69 62 72 61 |s, see t|he Libra|
|000029b0| 72 79 20 52 6f 75 74 69 | 6e 65 73 2e 20 20 0d 0d |ry Routi|nes.  ..|
|000029c0| 2d 20 2d 20 2d 20 2d 20 | 20 56 65 63 74 6f 72 73 |- - - - | Vectors|
|000029d0| 20 20 2d 20 2d 20 2d 20 | 2d 20 2d 0d 3f 20 41 20 |  - - - |- -.? A |
|000029e0| 3d 20 5b 32 2c 20 33 2c | 20 35 5d 3b 20 20 20 20 |= [2, 3,| 5];    |
|000029f0| 20 23 20 44 65 66 69 6e | 65 20 74 77 6f 20 33 2d | # Defin|e two 3-|
|00002a00| 44 20 76 65 63 74 6f 72 | 73 2e 0d 3f 20 42 20 3d |D vector|s..? B =|
|00002a10| 20 5b 31 2c 20 2d 31 2c | 20 32 5d 3b 0d 0d 23 20 | [1, -1,| 2];..# |
|00002a20| 41 64 64 69 6e 67 20 76 | 65 63 74 6f 72 73 20 63 |Adding v|ectors c|
|00002a30| 6f 6d 70 6f 6e 65 6e 74 | 20 62 79 20 63 6f 6d 70 |omponent| by comp|
|00002a40| 6f 6e 65 6e 74 2e 0d 3f | 20 41 20 2b 20 42 0d 20 |onent..?| A + B. |
|00002a50| 20 5b 33 2c 20 32 2c 20 | 37 5d 20 0d 0d 23 20 54 | [3, 2, |7] ..# T|
|00002a60| 68 65 20 64 6f 74 20 70 | 72 6f 64 75 63 74 20 6f |he dot p|roduct o|
|00002a70| 66 20 74 77 6f 20 76 65 | 63 74 6f 72 73 2e 20 28 |f two ve|ctors. (|
|00002a80| 54 6f 20 74 79 70 65 20 | 22 a5 22 20 75 73 65 20 |To type |"." use |
|00002a90| 6f 70 74 2d 38 20 6f 72 | 20 74 68 65 20 53 68 6f |opt-8 or| the Sho|
|00002aa0| 72 74 63 75 74 73 20 69 | 6e 20 74 68 65 20 4f 74 |rtcuts i|n the Ot|
|00002ab0| 68 65 72 20 6d 65 6e 75 | 2e 29 0d 3f 20 41 20 a5 |her menu|.).? A .|
|00002ac0| 20 42 0d 20 20 39 20 0d | 0d 23 20 41 20 66 75 6e | B.  9 .|.# A fun|
|00002ad0| 63 74 69 6f 6e 20 74 6f | 20 66 69 6e 64 20 74 68 |ction to| find th|
|00002ae0| 65 20 6c 65 6e 67 74 68 | 20 6f 66 20 61 20 76 65 |e length| of a ve|
|00002af0| 63 74 6f 72 3a 0d 3f 20 | 4c 65 6e 67 74 68 28 56 |ctor:.? |Length(V|
|00002b00| 29 20 3d 20 73 71 72 74 | 28 56 a5 56 29 3b 0d 3f |) = sqrt|(V.V);.?|
|00002b10| 20 4c 65 6e 67 74 68 28 | 41 29 0d 20 20 36 2e 31 | Length(|A).  6.1|
|00002b20| 36 34 34 31 34 20 0d 0d | 23 20 54 68 65 20 33 44 |64414 ..|# The 3D|
|00002b30| 20 63 72 6f 73 73 20 70 | 72 6f 64 75 63 74 3a 0d | cross p|roduct:.|
|00002b40| 3f 20 66 75 6e 63 74 69 | 6f 6e 20 43 72 6f 73 73 |? functi|on Cross|
|00002b50| 33 44 28 58 2c 59 29 20 | 20 23 20 52 65 74 75 72 |3D(X,Y) | # Retur|
|00002b60| 6e 73 20 74 68 65 20 33 | 44 20 63 72 6f 73 73 20 |ns the 3|D cross |
|00002b70| 70 72 6f 64 75 63 74 20 | 6f 66 20 74 77 6f 20 33 |product |of two 3|
|00002b80| 44 20 76 65 63 74 6f 72 | 73 20 78 2c 79 2e 0d 2e |D vector|s x,y...|
|00002b90| 20 20 20 76 61 72 20 5a | 0d 2e 20 20 20 23 20 20 |   var Z|..   #  |
|00002ba0| 49 6e 70 75 74 3a 20 20 | 20 58 2c 59 5b 31 c9 33 |Input:  | X,Y[1.3|
|00002bb0| 5d 20 33 2d 44 20 76 65 | 63 74 6f 72 73 0d 2e 20 |] 3-D ve|ctors.. |
|00002bc0| 20 20 23 20 20 4f 75 74 | 70 75 74 3a 20 43 72 6f |  #  Out|put: Cro|
|00002bd0| 73 73 33 44 20 3d 20 58 | 20 63 72 6f 73 73 20 59 |ss3D = X| cross Y|
|00002be0| 0d 2e 20 20 20 62 65 67 | 69 6e 0d 2e 20 20 20 20 |..   beg|in..    |
|00002bf0| 20 20 69 66 20 73 69 7a | 65 28 78 29 20 3c 3e 20 |  if siz|e(x) <> |
|00002c00| 33 20 74 68 65 6e 0d 2e | 20 20 20 20 20 20 20 20 |3 then..|        |
|00002c10| 43 72 6f 73 73 33 44 20 | 3d 20 22 20 45 52 52 4f |Cross3D |= " ERRO|
|00002c20| 52 3a 20 58 20 6d 75 73 | 74 20 62 65 20 61 20 33 |R: X mus|t be a 3|
|00002c30| 44 20 76 65 63 74 6f 72 | 20 66 6f 72 20 43 72 6f |D vector| for Cro|
|00002c40| 73 73 33 44 22 0d 2e 20 | 20 20 20 20 20 65 6c 73 |ss3D".. |     els|
|00002c50| 65 20 69 66 20 73 69 7a | 65 28 79 29 20 3c 3e 20 |e if siz|e(y) <> |
|00002c60| 33 20 74 68 65 6e 0d 2e | 20 20 20 20 20 20 20 20 |3 then..|        |
|00002c70| 20 43 72 6f 73 73 33 44 | 20 3d 20 22 20 45 52 52 | Cross3D| = " ERR|
|00002c80| 4f 52 3a 20 59 20 6d 75 | 73 74 20 62 65 20 61 20 |OR: Y mu|st be a |
|00002c90| 33 44 20 76 65 63 74 6f | 72 20 66 6f 72 20 43 72 |3D vecto|r for Cr|
|00002ca0| 6f 73 73 33 44 22 0d 2e | 20 20 20 20 20 20 65 6c |oss3D"..|      el|
|00002cb0| 73 65 0d 2e 20 20 20 20 | 20 20 62 65 67 69 6e 0d |se..    |  begin.|
|00002cc0| 2e 20 20 20 20 20 20 20 | 20 7a 5b 31 5d 20 3d 20 |.       | z[1] = |
|00002cd0| 78 5b 32 5d 20 79 5b 33 | 5d 20 2d 20 78 5b 33 5d |x[2] y[3|] - x[3]|
|00002ce0| 20 79 5b 32 5d 3b 0d 2e | 20 20 20 20 20 20 20 20 | y[2];..|        |
|00002cf0| 7a 5b 32 5d 20 3d 20 78 | 5b 33 5d 20 79 5b 31 5d |z[2] = x|[3] y[1]|
|00002d00| 20 2d 20 78 5b 31 5d 20 | 79 5b 33 5d 3b 0d 2e 20 | - x[1] |y[3];.. |
|00002d10| 20 20 20 20 20 20 20 7a | 5b 33 5d 20 3d 20 78 5b |       z|[3] = x[|
|00002d20| 31 5d 20 79 5b 32 5d 20 | 2d 20 78 5b 32 5d 20 79 |1] y[2] |- x[2] y|
|00002d30| 5b 31 5d 3b 0d 2e 20 20 | 20 20 20 20 20 20 43 72 |[1];..  |      Cr|
|00002d40| 6f 73 73 33 44 20 3d 20 | 7a 0d 2e 20 20 20 20 20 |oss3D = |z..     |
|00002d50| 20 65 6e 64 0d 2e 20 20 | 20 20 65 6e 64 0d 2e 20 | end..  |  end.. |
|00002d60| 20 20 20 0d 3f 20 0d 0d | 3f 20 43 72 6f 73 73 33 |   .? ..|? Cross3|
|00002d70| 44 28 41 2c 42 29 0d 20 | 20 5b 31 31 2c 20 31 2c |D(A,B). | [11, 1,|
|00002d80| 20 2d 35 5d 20 20 20 20 | 20 23 20 41 20 63 72 6f | -5]    | # A cro|
|00002d90| 73 73 20 42 2e 0d 0d 0d | 2d 20 2d 20 2d 20 2d 20 |ss B....|- - - - |
|00002da0| 20 4d 61 74 72 69 63 65 | 73 20 20 2d 20 2d 20 2d | Matrice|s  - - -|
|00002db0| 20 2d 20 2d 0d 0d 23 20 | 41 20 6d 61 74 72 69 78 | - -..# |A matrix|
|00002dc0| 20 69 73 20 6a 75 73 74 | 20 61 20 22 76 65 63 74 | is just| a "vect|
|00002dd0| 6f 72 20 6f 66 20 76 65 | 63 74 6f 72 73 22 2c 20 |or of ve|ctors", |
|00002de0| 61 6e 64 20 63 61 6e 20 | 62 65 20 65 6e 74 65 72 |and can |be enter|
|00002df0| 65 64 20 74 68 61 74 20 | 77 61 79 3a 0d 3f 20 47 |ed that |way:.? G|
|00002e00| 20 3d 20 5b 20 5b 32 2c | 33 5d 20 2c 20 5b 31 2c | = [ [2,|3] , [1,|
|00002e10| 30 5d 20 5d 20 20 20 20 | 20 20 23 20 44 65 66 69 |0] ]    |  # Defi|
|00002e20| 6e 65 20 61 20 6d 61 74 | 72 69 78 20 47 2e 0d 20 |ne a mat|rix G.. |
|00002e30| 20 47 5b 31 c9 32 2c 31 | c9 32 5d 20 3d 20 5b 5b | G[1.2,1|.2] = [[|
|00002e40| 32 2c 20 33 5d 2c 20 0d | 2e 20 20 20 20 20 20 20 |2, 3], .|.       |
|00002e50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 5b |        |       [|
|00002e60| 31 2c 20 30 5d 5d 20 20 | 2e 20 20 0d 0d 0d 23 20 |1, 0]]  |.  ...# |
|00002e70| 20 4e 6f 74 65 20 74 68 | 61 74 20 4e 43 49 49 20 | Note th|at NCII |
|00002e80| 6f 75 74 70 75 74 73 20 | 6d 61 74 72 69 63 65 73 |outputs |matrices|
|00002e90| 20 75 73 65 20 61 20 6d | 75 6c 74 69 2d 6c 69 6e | use a m|ulti-lin|
|00002ea0| 65 20 66 6f 72 6d 61 74 | 2c 20 61 6c 69 67 6e 69 |e format|, aligni|
|00002eb0| 6e 67 20 72 6f 77 73 2e | 20 20 54 68 65 20 70 65 |ng rows.|  The pe|
|00002ec0| 72 69 6f 64 20 61 74 20 | 74 68 65 20 73 74 61 72 |riod at |the star|
|00002ed0| 74 20 6f 66 20 74 68 65 | 20 73 65 63 6f 6e 64 20 |t of the| second |
|00002ee0| 72 6f 77 20 6d 61 72 6b | 73 20 61 20 6d 75 6c 74 |row mark|s a mult|
|00002ef0| 69 2d 6c 69 6e 65 20 62 | 6c 6f 63 6b 2c 20 77 68 |i-line b|lock, wh|
|00002f00| 69 63 68 20 69 73 20 65 | 76 61 6c 75 61 74 65 64 |ich is e|valuated|
|00002f10| 20 61 6c 6c 20 61 74 20 | 6f 6e 63 65 20 77 68 65 | all at |once whe|
|00002f20| 6e 20 74 68 65 20 6c 61 | 73 74 20 72 6f 77 20 69 |n the la|st row i|
|00002f30| 73 20 65 76 61 6c 75 61 | 74 65 64 2e 20 20 28 50 |s evalua|ted.  (P|
|00002f40| 72 6f 67 72 61 6d 73 20 | 61 6e 64 20 66 75 6e 63 |rograms |and func|
|00002f50| 74 69 6f 6e 73 20 75 73 | 65 20 74 68 65 20 73 61 |tions us|e the sa|
|00002f60| 6d 65 20 73 79 6e 74 61 | 78 29 2e 0d 0d 23 20 4d |me synta|x)...# M|
|00002f70| 61 74 72 69 63 65 73 20 | 63 61 6e 20 62 65 20 65 |atrices |can be e|
|00002f80| 6e 74 65 72 65 64 20 75 | 73 69 6e 67 20 74 68 65 |ntered u|sing the|
|00002f90| 73 65 20 64 6f 74 2c 20 | 74 6f 6f 2e 20 20 49 6e |se dot, |too.  In|
|00002fa0| 20 66 61 63 74 2c 20 69 | 66 20 61 20 72 6f 77 20 | fact, i|f a row |
|00002fb0| 69 73 20 74 79 70 65 64 | 20 61 6e 64 20 52 65 74 |is typed| and Ret|
|00002fc0| 75 72 6e 20 68 69 74 2c | 20 74 68 65 6e 20 4e 43 |urn hit,| then NC|
|00002fd0| 49 49 20 77 69 6c 6c 20 | 6f 75 74 70 75 74 20 74 |II will |output t|
|00002fe0| 68 65 20 70 65 72 69 6f | 64 20 74 6f 20 73 74 61 |he perio|d to sta|
|00002ff0| 72 74 20 74 68 65 20 6e | 65 78 74 20 72 6f 77 2e |rt the n|ext row.|
|00003000| 0d 3f 20 48 20 3d 20 5b | 20 5b 30 2c 2d 31 5d 2c |.? H = [| [0,-1],|
|00003010| 20 20 20 20 20 20 20 23 | 20 41 66 74 65 72 20 61 |       #| After a|
|00003020| 20 52 65 74 75 72 6e 20 | 68 65 72 65 2c 0d 2e 20 | Return |here,.. |
|00003030| 20 20 20 20 20 20 20 20 | 20 20 20 5b 31 2c 30 5d |        |   [1,0]|
|00003040| 2c 20 20 20 20 20 20 23 | 20 4e 43 20 70 75 74 20 |,      #| NC put |
|00003050| 74 68 65 20 70 65 72 69 | 6f 64 20 61 74 20 74 68 |the peri|od at th|
|00003060| 65 20 73 74 61 72 74 20 | 6f 66 20 74 68 69 73 20 |e start |of this |
|00003070| 72 6f 77 2e 0d 2e 20 20 | 20 20 20 20 20 20 20 20 |row...  |        |
|00003080| 20 20 5b 30 2c 31 5d 20 | 5d 20 20 20 20 20 20 23 |  [0,1] |]      #|
|00003090| 20 41 20 70 65 72 69 6f | 64 20 61 6c 6f 6e 65 20 | A perio|d alone |
|000030a0| 6f 6e 20 61 20 72 6f 77 | 20 28 6f 72 20 61 74 20 |on a row| (or at |
|000030b0| 74 68 65 20 65 6e 64 20 | 6f 66 20 6c 69 6e 65 29 |the end |of line)|
|000030c0| 20 65 6e 64 73 20 74 68 | 65 20 6d 75 6c 74 69 2d | ends th|e multi-|
|000030d0| 6c 69 6e 65 20 62 6c 6f | 63 6b 2e 2e 20 20 20 20 |line blo|ck..    |
|000030e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000030f0| 20 0d 2e 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | ..     |        |
|00003100| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 0d 3f |        |      .?|
|00003110| 20 48 0d 20 20 48 5b 31 | c9 33 2c 31 c9 32 5d 20 | H.  H[1|.3,1.2] |
|00003120| 3d 20 5b 5b 30 2c 20 2d | 31 5d 2c 20 0d 2e 20 20 |= [[0, -|1], ..  |
|00003130| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003140| 20 20 20 20 5b 31 2c 20 | 30 5d 2c 20 0d 2e 20 20 |    [1, |0], ..  |
|00003150| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003160| 20 20 20 20 5b 30 2c 20 | 31 5d 5d 20 20 2e 20 20 |    [0, |1]]  .  |
|00003170| 0d 0d 23 20 4d 61 74 72 | 69 63 65 73 20 6d 61 79 |..# Matr|ices may|
|00003180| 20 61 6c 73 6f 20 62 65 | 20 65 6e 74 65 72 65 64 | also be| entered|
|00003190| 20 75 73 69 6e 67 20 22 | 3b 22 20 74 6f 20 73 65 | using "|;" to se|
|000031a0| 70 65 72 61 74 65 20 74 | 68 65 20 72 6f 77 73 2c |perate t|he rows,|
|000031b0| 20 77 69 74 68 20 6e 6f | 20 69 6e 74 65 72 6e 61 | with no| interna|
|000031c0| 6c 20 62 72 61 63 65 73 | 2e 0d 3f 20 49 64 65 6e |l braces|..? Iden|
|000031d0| 74 69 74 79 20 3d 20 5b | 31 2c 30 20 3b 20 30 2c |tity = [|1,0 ; 0,|
|000031e0| 31 5d 0d 20 20 49 64 65 | 6e 74 69 74 79 5b 31 c9 |1].  Ide|ntity[1.|
|000031f0| 32 2c 31 c9 32 5d 20 3d | 20 5b 5b 31 2c 20 30 5d |2,1.2] =| [[1, 0]|
|00003200| 2c 20 0d 2e 20 20 20 20 | 20 20 20 20 20 20 20 20 |, ..    |        |
|00003210| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003220| 20 20 20 5b 30 2c 20 31 | 5d 5d 20 20 2e 20 20 0d |   [0, 1|]]  .  .|
|00003230| 0d 23 20 54 68 69 73 20 | 28 61 6e 64 20 61 6c 6c |.# This |(and all|
|00003240| 20 6d 61 74 72 69 63 65 | 73 20 61 6e 64 20 74 65 | matrice|s and te|
|00003250| 6e 73 6f 72 73 29 20 6d | 61 79 20 62 65 20 74 72 |nsors) m|ay be tr|
|00003260| 65 61 74 65 64 20 61 73 | 20 61 20 31 44 20 61 72 |eated as| a 1D ar|
|00003270| 72 61 79 20 62 79 20 4a | 5b 5d 20 6f 72 20 4a 5b |ray by J|[] or J[|
|00003280| 69 5d 3a 0d 3f 20 49 64 | 65 6e 74 69 74 79 5b 5d |i]:.? Id|entity[]|
|00003290| 0d 20 20 5b 31 2c 20 30 | 2c 20 30 2c 20 31 5d 20 |.  [1, 0|, 0, 1] |
|000032a0| 0d 0d 23 20 54 6f 20 6d | 61 74 72 69 78 2d 6d 75 |..# To m|atrix-mu|
|000032b0| 6c 74 69 70 6c 79 20 74 | 77 6f 20 6d 61 74 72 69 |ltiply t|wo matri|
|000032c0| 63 65 73 20 28 69 2e 65 | 2e 2e 20 41 5b 69 2c 6a |ces (i.e|.. A[i,j|
|000032d0| 5d 20 3d 20 73 75 6d 20 | 6f 76 65 72 20 6b 20 20 |] = sum |over k  |
|000032e0| 42 5b 69 2c 6b 5d 20 43 | 5b 6b 2c 6a 5d 20 29 20 |B[i,k] C|[k,j] ) |
|000032f0| 2c 20 61 20 73 75 6d 20 | 69 73 20 70 65 72 66 6f |, a sum |is perfo|
|00003300| 72 6d 65 64 20 6f 76 65 | 72 20 22 61 64 6a 61 63 |rmed ove|r "adjac|
|00003310| 65 6e 74 22 20 69 6e 64 | 65 63 65 73 20 6b 2e 20 |ent" ind|eces k. |
|00003320| 54 68 65 20 64 6f 74 20 | 70 72 6f 64 75 63 74 20 |The dot |product |
|00003330| 28 a5 29 20 64 6f 65 73 | 20 74 68 69 73 20 69 6e |(.) does| this in|
|00003340| 20 4e 43 49 49 2e 20 28 | 53 65 65 20 61 62 6f 76 | NCII. (|See abov|
|00003350| 65 2e 29 0d 3f 20 47 0d | 20 20 47 5b 31 c9 32 2c |e.).? G.|  G[1.2,|
|00003360| 31 c9 32 5d 20 3d 20 5b | 5b 32 2c 20 33 5d 2c 20 |1.2] = [|[2, 3], |
|00003370| 0d 2e 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|00003380| 20 20 20 20 20 20 20 20 | 5b 31 2c 20 30 5d 5d 20 |        |[1, 0]] |
|00003390| 20 2e 20 20 0d 3f 20 49 | 64 65 6e 74 69 74 79 20 | .  .? I|dentity |
|000033a0| a5 20 47 20 20 20 23 20 | 54 68 65 20 69 64 65 6e |. G   # |The iden|
|000033b0| 74 69 74 79 20 6d 61 74 | 72 69 78 20 74 69 6d 65 |tity mat|rix time|
|000033c0| 73 20 61 6e 6f 74 68 65 | 72 20 6d 61 74 72 69 78 |s anothe|r matrix|
|000033d0| 20 69 73 0d 20 20 5b 5b | 32 2c 20 33 5d 2c 20 0d | is.  [[|2, 3], .|
|000033e0| 2e 20 20 5b 31 2c 20 30 | 5d 5d 20 20 2e 20 20 20 |.  [1, 0|]]  .   |
|000033f0| 20 23 20 74 68 65 20 73 | 61 6d 65 20 6d 61 74 72 | # the s|ame matr|
|00003400| 69 78 2e 0d 0d 23 20 4d | 61 74 72 69 78 2d 56 65 |ix...# M|atrix-Ve|
|00003410| 63 74 6f 72 20 6d 75 6c | 74 69 70 6c 69 63 61 74 |ctor mul|tiplicat|
|00003420| 69 6f 6e 20 77 6f 72 6b | 73 20 74 68 65 20 73 61 |ion work|s the sa|
|00003430| 6d 65 20 77 61 79 3a 0d | 3f 20 41 0d 20 20 41 5b |me way:.|? A.  A[|
|00003440| 31 c9 33 5d 20 3d 20 5b | 32 2c 20 33 2c 20 35 5d |1.3] = [|2, 3, 5]|
|00003450| 20 0d 3f 20 47 0d 20 20 | 47 5b 31 c9 32 2c 31 c9 | .? G.  |G[1.2,1.|
|00003460| 32 5d 20 3d 20 5b 5b 32 | 2c 20 33 5d 2c 20 0d 2e |2] = [[2|, 3], ..|
|00003470| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003480| 20 20 20 20 20 20 5b 31 | 2c 20 30 5d 5d 20 20 2e |      [1|, 0]]  .|
|00003490| 20 20 0d 0d 0d 23 20 22 | 4e 6f 72 6d 61 6c 22 20 |  ...# "|Normal" |
|000034a0| 6d 75 6c 74 69 70 6c 69 | 63 61 74 69 6f 6e 20 69 |multipli|cation i|
|000034b0| 6e 20 4e 43 49 49 2c 20 | 6f 6e 20 74 68 65 20 6f |n NCII, |on the o|
|000034c0| 74 68 65 72 20 68 61 6e | 64 2c 20 6d 75 6c 74 69 |ther han|d, multi|
|000034d0| 70 6c 69 65 73 20 65 6c | 65 6d 65 6e 74 2d 62 79 |plies el|ement-by|
|000034e0| 2d 65 6c 65 6d 65 6e 74 | 2e 0d 3f 20 49 64 65 6e |-element|..? Iden|
|000034f0| 74 69 74 79 20 2a 20 47 | 20 20 20 20 20 20 20 23 |tity * G|       #|
|00003500| 20 3d 20 41 6e 73 77 65 | 72 5b 69 2c 6a 5d 20 3d | = Answe|r[i,j] =|
|00003510| 20 49 64 65 6e 74 69 74 | 79 5b 69 2c 6a 5d 20 2a | Identit|y[i,j] *|
|00003520| 20 47 5b 69 2c 6a 5d 2e | 0d 20 20 5b 5b 32 2c 20 | G[i,j].|.  [[2, |
|00003530| 30 5d 2c 20 0d 2e 20 20 | 5b 30 2c 20 30 5d 5d 20 |0], ..  |[0, 0]] |
|00003540| 20 2e 20 20 0d 0d 0d 23 | 20 53 75 70 70 6f 73 65 | .  ...#| Suppose|
|00003550| 20 6e 6f 77 20 74 68 61 | 74 20 77 65 20 77 69 73 | now tha|t we wis|
|00003560| 68 20 74 6f 20 64 65 66 | 69 6e 65 20 61 20 73 71 |h to def|ine a sq|
|00003570| 75 61 72 65 20 33 78 33 | 20 6d 61 74 72 69 78 20 |uare 3x3| matrix |
|00003580| 42 5b 69 2c 6a 5d 20 3d | 20 33 20 69 20 2b 20 32 |B[i,j] =| 3 i + 2|
|00003590| 20 6a 5e 32 2e 20 20 59 | 6f 75 20 6d 69 67 68 74 | j^2.  Y|ou might|
|000035a0| 20 74 68 69 6e 6b 20 74 | 68 61 74 20 74 68 69 73 | think t|hat this|
|000035b0| 20 73 68 6f 75 6c 64 20 | 77 6f 72 6b 3a 0d 3f 20 | should |work:.? |
|000035c0| 69 20 3d 20 31 c9 33 3b | 20 6a 20 3d 20 31 c9 33 |i = 1.3;| j = 1.3|
|000035d0| 3b 0d 3f 20 42 5b 69 2c | 6a 5d 20 3d 20 33 20 69 |;.? B[i,|j] = 3 i|
|000035e0| 20 2b 20 32 20 6a 5e 32 | 20 20 20 20 20 20 20 20 | + 2 j^2|        |
|000035f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 23 20 54 68 |        |    # Th|
|00003600| 69 73 20 64 6f 65 73 6e | 27 74 20 77 6f 72 6b 2e |is doesn|'t work.|
|00003610| 0d 20 20 42 5b 31 c9 33 | 2c 31 c9 33 5d 20 3d 20 |.  B[1.3|,1.3] = |
|00003620| 5b 5b 35 2c 20 31 34 2c | 20 32 37 5d 2c 20 0d 2e |[[5, 14,| 27], ..|
|00003630| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003640| 20 20 20 20 20 20 5b 35 | 2c 20 31 34 2c 20 32 37 |      [5|, 14, 27|
|00003650| 5d 2c 20 0d 2e 20 20 20 | 20 20 20 20 20 20 20 20 |], ..   |        |
|00003660| 20 20 20 20 20 20 20 20 | 20 20 20 5b 35 2c 20 31 |        |   [5, 1|
|00003670| 34 2c 20 32 37 5d 5d 20 | 20 2e 20 20 0d 23 20 42 |4, 27]] | .  .# B|
|00003680| 55 54 2c 20 69 74 20 64 | 6f 65 73 6e 27 74 2e 20 |UT, it d|oesn't. |
|00003690| 20 54 68 65 20 72 65 61 | 73 6f 6e 20 69 73 20 74 | The rea|son is t|
|000036a0| 68 65 20 72 69 67 68 74 | 20 68 61 6e 64 20 73 69 |he right| hand si|
|000036b0| 64 65 20 69 73 20 6e 6f | 74 20 61 20 6d 61 74 72 |de is no|t a matr|
|000036c0| 69 78 3b 20 69 74 20 69 | 73 20 69 6e 73 74 65 61 |ix; it i|s instea|
|000036d0| 64 0d 20 33 20 69 20 2b | 20 32 20 6a 5e 32 20 3d |d. 3 i +| 2 j^2 =|
|000036e0| 20 20 33 20 2a 20 5b 31 | 2c 32 2c 33 5d 20 2b 20 |  3 * [1|,2,3] + |
|000036f0| 32 20 2a 20 5b 31 2c 34 | 2c 39 5d 20 3d 20 5b 35 |2 * [1,4|,9] = [5|
|00003700| 2c 31 34 2c 32 37 5d 2e | 20 20 57 68 65 6e 20 74 |,14,27].|  When t|
|00003710| 68 65 20 33 78 33 20 6d | 61 74 72 69 78 20 42 5b |he 3x3 m|atrix B[|
|00003720| 31 c9 33 2c 20 31 c9 33 | 5d 20 69 73 20 73 65 74 |1.3, 1.3|] is set|
|00003730| 20 74 6f 20 74 68 69 73 | 2c 20 6d 75 6c 74 69 70 | to this|, multip|
|00003740| 6c 65 20 63 6f 70 69 65 | 73 20 6f 66 20 74 68 65 |le copie|s of the|
|00003750| 20 72 69 67 68 74 20 68 | 61 6e 64 20 73 69 64 65 | right h|and side|
|00003760| 20 61 72 65 20 63 6f 70 | 69 65 64 20 69 6e 2e 0d | are cop|ied in..|
|00003770| 0d 23 20 4f 6e 65 20 77 | 61 79 20 74 68 61 74 20 |.# One w|ay that |
|00003780| 77 6f 72 6b 73 20 69 73 | 20 74 6f 20 75 73 65 20 |works is| to use |
|00003790| 61 20 64 6f 75 62 6c 65 | 20 46 4f 52 20 6c 6f 6f |a double| FOR loo|
|000037a0| 70 2c 20 77 69 74 68 20 | 22 26 22 20 74 6f 20 6c |p, with |"&" to l|
|000037b0| 6f 6f 70 20 6f 76 65 72 | 20 74 77 6f 20 69 6e 64 |oop over| two ind|
|000037c0| 65 63 65 73 3a 0d 3f 20 | 66 6f 72 20 69 20 26 20 |eces:.? |for i & |
|000037d0| 6a 20 64 6f 20 42 5b 69 | 2c 6a 5d 20 3d 20 33 20 |j do B[i|,j] = 3 |
|000037e0| 69 20 2b 20 32 20 6a 5e | 32 0d 20 20 42 5b 31 c9 |i + 2 j^|2.  B[1.|
|000037f0| 33 2c 31 c9 33 5d 20 3d | 20 5b 5b 35 2c 20 31 31 |3,1.3] =| [[5, 11|
|00003800| 2c 20 32 31 5d 2c 20 0d | 2e 20 20 20 20 20 20 20 |, 21], .|.       |
|00003810| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 5b |        |       [|
|00003820| 38 2c 20 31 34 2c 20 32 | 34 5d 2c 20 0d 2e 20 20 |8, 14, 2|4], ..  |
|00003830| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003840| 20 20 20 20 5b 31 31 2c | 20 31 37 2c 20 32 37 5d |    [11,| 17, 27]|
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|00004660| 00 0a 00 03 00 00 00 09 | 00 00 00 00 00 00 00 00 |........|........|
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|000046d0| 00 00 00 00 05 7b 00 0c | 00 0a 00 03 00 00 00 09 |.....{..|........|
|000046e0| 00 00 00 00 00 00 00 00 | 07 0f 00 0e 00 0b 00 03 |........|........|
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|00004710| 08 1d 00 0e 00 0b 00 03 | 08 00 00 09 00 00 00 00 |........|........|
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|000048f0| 0b 11 00 0c 00 0a 00 03 | 01 00 00 09 00 00 00 00 |........|........|
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|00004910| 00 00 00 00 00 00 00 00 | 0b 46 00 0e 00 0b 00 03 |........|.F......|
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|00004b10| 00 0b 00 03 08 00 00 09 | 00 00 00 00 00 00 00 00 |........|........|
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|00004ba0| 00 00 00 09 00 00 00 00 | 00 00 00 00 11 94 00 0e |........|........|
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|00004c20| 00 00 00 00 12 f8 00 0c | 00 0a 00 03 00 00 00 09 |........|........|
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|00004c70| 00 00 00 00 13 59 00 0c | 00 0a 00 03 00 00 00 09 |.....Y..|........|
|00004c80| 00 00 00 00 00 00 00 00 | 13 ab 00 0c 00 0a 00 03 |........|........|
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|00004d20| 00 00 00 00 00 00 00 00 | 15 04 00 0c 00 0a 00 03 |........|........|
|00004d30| 01 00 00 09 00 00 00 00 | 00 00 00 00 15 41 00 0e |........|.....A..|
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|00004d60| 00 00 00 00 15 67 00 0c | 00 0a 00 03 01 00 00 09 |.....g..|........|
|00004d70| 00 00 00 00 00 00 00 00 | 15 83 00 0e 00 0b 00 03 |........|........|
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|00004de0| 00 0a 00 03 01 00 00 09 | 00 00 00 00 00 00 00 00 |........|........|
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|00004e30| 00 0a 00 03 00 00 00 09 | 00 00 00 00 00 00 00 00 |........|........|
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|00004e50| 00 00 00 00 17 48 00 0e | 00 0b 00 03 08 00 00 09 |.....H..|........|
|00004e60| 00 00 00 00 00 00 00 00 | 17 49 00 0c 00 0a 00 03 |........|.I......|
|00004e70| 00 00 00 09 00 00 00 00 | 00 00 00 00 17 71 00 0c |........|.....q..|
|00004e80| 00 0a 00 03 01 00 00 09 | 00 00 00 00 00 00 00 00 |........|........|
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|00004ea0| 00 00 00 00 17 e5 00 0e | 00 0b 00 03 08 00 00 09 |........|........|
|00004eb0| 00 00 00 00 00 00 00 00 | 17 e6 00 0c 00 0a 00 03 |........|........|
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|00004ed0| 00 0a 00 03 04 00 00 09 | 00 00 00 00 00 00 00 00 |........|........|
|00004ee0| 17 f5 00 0c 00 0a 00 03 | 00 00 00 09 00 00 00 00 |........|........|
|00004ef0| 00 00 00 00 19 a4 00 0e | 00 0b 00 03 08 00 00 09 |........|........|
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|00004f20| 00 0a 00 03 01 00 00 09 | 00 00 00 00 00 00 00 00 |........|........|
|00004f30| 19 d3 00 0c 00 0a 00 03 | 00 00 00 09 00 00 00 00 |........|........|
|00004f40| 00 00 00 00 1a 41 00 0c | 00 0a 00 03 01 00 00 09 |.....A..|........|
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|00004f90| 01 00 01 55 81 55 01 55 | 00 00 00 00 00 00 00 00 |...U.U.U|........|
|00004fa0| 00 04 00 0a 00 00 09 0a | 00 0c 00 00 09 0c 00 0e |........|........|
|00004fb0| 14 56 65 63 74 6f 72 73 | 20 61 6e 64 20 4d 61 74 |.Vectors| and Mat|
|00004fc0| 72 69 63 65 73 73 02 00 | 00 00 4e 64 63 32 4e 43 |ricess..|..Ndc2NC|
|00004fd0| 00 00 4e 64 63 32 4e 43 | 49 49 00 00 00 00 00 00 |..Ndc2NC|II......|
|00004fe0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
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|00005010| 0c 7a 02 8f 04 28 03 85 | 06 b8 08 51 03 85 04 7a |.z...(..|...Q...z|
|00005020| 03 85 05 70 06 14 07 0a | 07 0a 07 0a 07 0a 07 0a |...p....|........|
|00005030| 07 0a 07 0a 07 0a 07 0a | 04 28 03 d7 08 51 08 51 |........|.(...Q.Q|
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|00005070| 0a 3d 0e 14 08 f5 08 f5 | 09 eb 03 d7 07 ae 05 1e |.=......|........|
|00005080| 00 00 01 00 00 00 01 00 | 00 00 00 00 00 00 00 1e |........|........|
|00005090| 00 00 00 00 00 00 00 00 | 00 1c 00 1e ff ff 00 00 |........|........|
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|000050f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
+--------+-------------------------+-------------------------+--------+--------+