home *** CD-ROM | disk | FTP | other *** search
/ Interactive Algebra & Tri…f Guided Study Companion / Interactive Algebra and Trigonometry - A Self-Guided Study Companion.iso / tutor / chap_10 / 10-3-1.tut < prev    next >
Unknown  |  1996-10-21  |  3.0 KB
open in: MacOS 8.1     |     Win98     |     DOS

view JSON data     |     view as text


This file was not able to be converted.
This format is not currently supported by dexvert.

ConfidenceProgramDetectionMatch TypeSupport
1% dexvert Eclipse Tutorial (other/eclipseTutorial) ext Unsupported
1% dexvert JuggleKrazy Tutorial (other/juggleKrazyTutorial) ext Unsupported
100% file data default
100% gt2 Kopftext: 'TUTOR 06w' default (weak)


hex view
+--------+-------------------------+-------------------------+--------+--------+
|00000000| 54 55 54 4f 52 20 30 36 | 77 0b 00 00 6e 00 00 00 |TUTOR 06|w...n...|
|00000010| 53 65 63 74 69 6f 6e 20 | 31 30 2e 33 20 20 54 68 |Section |10.3  Th|
|00000020| 65 20 49 6e 76 65 72 73 | 65 20 6f 66 20 61 20 53 |e Invers|e of a S|
|00000030| 71 75 61 72 65 20 4d 61 | 74 72 69 78 0d 0b 00 46 |quare Ma|trix...F|
|00000040| 6f 72 20 6d 6f 72 65 20 | 70 72 61 63 74 69 63 65 |or more |practice|
|00000050| 3a 0d 0a 00 0d 0a 00 20 | 20 20 20 20 10 31 30 2d |:...... |    .10-|
|00000060| 33 2d 33 0e 78 31 30 2d | 33 0e 45 78 65 72 63 69 |3-3.x10-|3.Exerci|
|00000070| 73 65 73 0f 0d 0a 00 20 | 20 20 20 20 10 31 30 2d |ses.... |    .10-|
|00000080| 33 2d 32 0e 65 31 30 2d | 33 0e 47 75 69 64 65 64 |3-2.e10-|3.Guided|
|00000090| 20 45 78 65 72 63 69 73 | 65 73 0f 0d 0a 00 0d 0a | Exercis|es......|
|000000a0| 00 54 6f 70 69 63 73 20 | 66 6f 72 20 65 78 70 6c |.Topics |for expl|
|000000b0| 6f 72 61 74 69 6f 6e 3a | 0d 0a 00 0d 0a 00 20 20 |oration:|......  |
|000000c0| 20 20 20 0e 73 31 30 2d | 33 2d 31 0e 44 65 66 69 |   .s10-|3-1.Defi|
|000000d0| 6e 69 74 69 6f 6e 20 6f | 66 20 61 6e 20 49 6e 76 |nition o|f an Inv|
|000000e0| 65 72 73 65 20 6f 66 20 | 61 20 4d 61 74 72 69 78 |erse of |a Matrix|
|000000f0| 0f 0d 0a 00 20 20 20 20 | 20 0e 73 31 30 2d 33 2d |....    | .s10-3-|
|00000100| 32 0e 46 69 6e 64 69 6e | 67 20 74 68 65 20 49 6e |2.Findin|g the In|
|00000110| 76 65 72 73 65 20 6f 66 | 20 61 20 4d 61 74 72 69 |verse of| a Matri|
|00000120| 78 20 62 79 20 47 61 75 | 73 73 2d 4a 6f 72 64 61 |x by Gau|ss-Jorda|
|00000130| 6e 20 45 6c 69 6d 69 6e | 61 74 69 6f 6e 0f 0d 0a |n Elimin|ation...|
|00000140| 00 20 20 20 20 20 0e 73 | 31 30 2d 33 2d 33 0e 53 |.     .s|10-3-3.S|
|00000150| 79 73 74 65 6d 73 20 6f | 66 20 45 71 75 61 74 69 |ystems o|f Equati|
|00000160| 6f 6e 73 20 77 69 74 68 | 20 55 6e 69 71 75 65 20 |ons with| Unique |
|00000170| 53 6f 6c 75 74 69 6f 6e | 73 0f 0d 0a 00 53 65 63 |Solution|s....Sec|
|00000180| 74 69 6f 6e 20 31 30 2e | 33 20 20 54 68 65 20 49 |tion 10.|3  The I|
|00000190| 6e 76 65 72 73 65 20 6f | 66 20 61 20 53 71 75 61 |nverse o|f a Squa|
|000001a0| 72 65 20 4d 61 74 72 69 | 78 20 20 20 20 20 20 20 |re Matri|x       |
|000001b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000001c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000001d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000001e0| 20 20 20 20 20 20 20 20 | 20 11 32 2d 31 0d 0b 00 |        | .2-1...|
|000001f0| 11 31 4c 65 74 20 11 33 | 41 20 11 31 62 65 20 61 |.1Let .3|A .1be a|
|00000200| 20 73 71 75 61 72 65 20 | 6d 61 74 72 69 78 20 6f | square |matrix o|
|00000210| 66 20 6f 72 64 65 72 20 | 11 33 6e 11 31 2e 20 20 |f order |.3n.1.  |
|00000220| 49 66 20 74 68 65 72 65 | 20 65 78 69 73 74 73 20 |If there| exists |
|00000230| 61 20 6d 61 74 72 69 78 | 20 11 33 41 20 20 20 11 |a matrix| .3A   .|
|00000240| 31 73 75 63 68 20 74 68 | 61 74 20 0d 0a 00 20 20 |1such th|at ...  |
|00000250| 20 20 20 20 20 11 32 2d | 31 20 20 20 20 20 20 20 |     .2-|1       |
|00000260| 20 20 2d 31 0d 0b 00 20 | 20 20 20 20 11 33 41 41 |  -1... |    .3AA|
|00000270| 20 20 20 3d 20 49 20 20 | 3d 20 41 20 20 41 0d 0b |   = I  |= A  A..|
|00000280| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 |.       |      .2|
|00000290| 6e 0d 0b 00 20 20 20 20 | 20 20 2d 31 20 20 20 20 |n...    |  -1    |
|000002a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000002b0| 20 20 20 20 20 20 20 20 | 20 20 20 2d 31 0d 0b 00 |        |   -1...|
|000002c0| 11 31 74 68 65 6e 20 11 | 33 41 20 20 20 11 31 69 |.1then .|3A   .1i|
|000002d0| 73 20 63 61 6c 6c 65 64 | 20 74 68 65 20 12 31 69 |s called| the .1i|
|000002e0| 6e 76 65 72 73 65 12 30 | 20 6f 66 20 11 33 41 11 |nverse.0| of .3A.|
|000002f0| 31 2e 20 20 11 33 41 20 | 20 20 11 31 69 73 20 72 |1.  .3A |  .1is r|
|00000300| 65 61 64 20 22 11 33 41 | 20 11 31 69 6e 76 65 72 |ead ".3A| .1inver|
|00000310| 73 65 2e 22 0d 0a 00 0d | 0a 00 49 66 20 61 20 6d |se."....|..If a m|
|00000320| 61 74 72 69 78 20 11 33 | 41 20 11 31 68 61 73 20 |atrix .3|A .1has |
|00000330| 61 6e 20 69 6e 76 65 72 | 73 65 2c 20 74 68 65 6e |an inver|se, then|
|00000340| 20 11 33 41 20 11 31 69 | 73 20 63 61 6c 6c 65 64 | .3A .1i|s called|
|00000350| 20 12 31 69 6e 76 65 72 | 74 69 62 6c 65 12 30 20 | .1inver|tible.0 |
|00000360| 28 6f 72 20 12 31 6e 6f | 6e 73 69 6e 67 75 6c 61 |(or .1no|nsingula|
|00000370| 72 12 30 29 3b 20 0d 0a | 00 6f 74 68 65 72 77 69 |r.0); ..|.otherwi|
|00000380| 73 65 2c 20 11 33 41 20 | 11 31 69 73 20 63 61 6c |se, .3A |.1is cal|
|00000390| 6c 65 64 20 12 31 73 69 | 6e 67 75 6c 61 72 12 30 |led .1si|ngular.0|
|000003a0| 2e 20 20 4e 6f 74 65 20 | 74 68 61 74 20 6f 6e 6c |.  Note |that onl|
|000003b0| 79 20 73 71 75 61 72 65 | 20 6d 61 74 72 69 63 65 |y square| matrice|
|000003c0| 73 20 63 61 6e 20 68 61 | 76 65 20 61 6e 20 0d 0a |s can ha|ve an ..|
|000003d0| 00 69 6e 76 65 72 73 65 | 2e 20 20 46 75 72 74 68 |.inverse|.  Furth|
|000003e0| 65 72 6d 6f 72 65 2c 20 | 69 66 20 61 20 6d 61 74 |ermore, |if a mat|
|000003f0| 72 69 78 20 68 61 73 20 | 61 6e 20 69 6e 76 65 72 |rix has |an inver|
|00000400| 73 65 2c 20 74 68 65 6e | 20 74 68 61 74 20 69 6e |se, then| that in|
|00000410| 76 65 72 73 65 20 69 73 | 20 0d 0a 00 75 6e 69 71 |verse is| ...uniq|
|00000420| 75 65 2e 0d 0a 00 53 65 | 63 74 69 6f 6e 20 31 30 |ue....Se|ction 10|
|00000430| 2e 33 20 20 54 68 65 20 | 49 6e 76 65 72 73 65 20 |.3  The |Inverse |
|00000440| 6f 66 20 61 20 53 71 75 | 61 72 65 20 4d 61 74 72 |of a Squ|are Matr|
|00000450| 69 78 0d 0b 00 4c 65 74 | 20 11 33 41 20 11 31 62 |ix...Let| .3A .1b|
|00000460| 65 20 61 20 73 71 75 61 | 72 65 20 6d 61 74 72 69 |e a squa|re matri|
|00000470| 78 20 6f 66 20 6f 72 64 | 65 72 20 11 33 6e 11 31 |x of ord|er .3n.1|
|00000480| 2e 20 20 54 68 65 6e 20 | 77 65 20 63 61 6e 20 12 |.  Then |we can .|
|00000490| 31 66 69 6e 64 20 74 68 | 65 20 69 6e 76 65 72 73 |1find th|e invers|
|000004a0| 65 20 6f 66 20 11 33 41 | 11 31 12 30 20 28 69 66 |e of .3A|.1.0 (if|
|000004b0| 20 0d 0a 00 69 74 20 65 | 78 69 73 74 73 29 20 61 | ...it e|xists) a|
|000004c0| 73 20 66 6f 6c 6c 6f 77 | 73 2e 0d 0a 00 0d 0a 00 |s follow|s.......|
|000004d0| 20 31 20 20 57 72 69 74 | 65 20 74 68 65 20 11 33 | 1  Writ|e the .3|
|000004e0| 6e 20 11 34 78 20 11 33 | 32 6e 20 11 31 6d 61 74 |n .4x .3|2n .1mat|
|000004f0| 72 69 78 20 74 68 61 74 | 20 63 6f 6e 73 69 73 74 |rix that| consist|
|00000500| 73 20 6f 66 20 74 68 65 | 20 67 69 76 65 6e 20 6d |s of the| given m|
|00000510| 61 74 72 69 78 20 11 33 | 41 20 11 31 6f 6e 20 74 |atrix .3|A .1on t|
|00000520| 68 65 20 6c 65 66 74 20 | 0d 0a 00 20 20 20 20 20 |he left |...     |
|00000530| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000540| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000550| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000560| 20 20 20 20 20 20 20 20 | 20 12 31 2e 12 30 0d 0b |        | .1..0..|
|00000570| 00 20 20 20 20 61 6e 64 | 20 74 68 65 20 11 33 6e |.    and| the .3n|
|00000580| 20 11 34 78 20 11 33 6e | 20 11 31 69 64 65 6e 74 | .4x .3n| .1ident|
|00000590| 69 74 79 20 6d 61 74 72 | 69 78 20 11 33 49 20 11 |ity matr|ix .3I .|
|000005a0| 31 6f 6e 20 74 68 65 20 | 72 69 67 68 74 20 74 6f |1on the |right to|
|000005b0| 20 6f 62 74 61 69 6e 20 | 5b 11 33 41 20 11 31 12 | obtain |[.3A .1.|
|000005c0| 31 2e 12 30 20 11 33 49 | 5d 11 31 2e 20 20 4e 6f |1..0 .3I|].1.  No|
|000005d0| 74 65 20 74 68 61 74 0d | 0a 00 0d 0b 00 20 20 20 |te that.|.....   |
|000005e0| 20 77 65 20 73 65 70 61 | 72 61 74 65 20 74 68 65 | we sepa|rate the|
|000005f0| 20 6d 61 74 72 69 63 65 | 73 20 11 33 41 20 11 31 | matrice|s .3A .1|
|00000600| 61 6e 64 20 11 33 49 20 | 11 31 62 79 20 61 20 64 |and .3I |.1by a d|
|00000610| 6f 74 74 65 64 20 6c 69 | 6e 65 2e 20 20 57 65 20 |otted li|ne.  We |
|00000620| 63 61 6c 6c 20 74 68 69 | 73 20 70 72 6f 63 65 73 |call thi|s proces|
|00000630| 73 20 0d 0a 00 0d 0b 00 | 20 20 20 20 12 31 61 64 |s ......|    .1ad|
|00000640| 6a 6f 69 6e 69 6e 67 12 | 30 20 74 68 65 20 6d 61 |joining.|0 the ma|
|00000650| 74 72 69 63 65 73 20 11 | 33 41 20 11 31 61 6e 64 |trices .|3A .1and|
|00000660| 20 11 33 49 11 31 2e 0d | 0a 00 0d 0a 00 20 32 2e | .3I.1..|..... 2.|
|00000670| 20 49 66 20 70 6f 73 73 | 69 62 6c 65 2c 20 72 6f | If poss|ible, ro|
|00000680| 77 20 72 65 64 75 63 65 | 20 11 33 41 20 11 31 74 |w reduce| .3A .1t|
|00000690| 6f 20 11 33 49 20 11 31 | 75 73 69 6e 67 20 65 6c |o .3I .1|using el|
|000006a0| 65 6d 65 6e 74 61 72 79 | 20 72 6f 77 20 6f 70 65 |ementary| row ope|
|000006b0| 72 61 74 69 6f 6e 73 20 | 6f 6e 20 74 68 65 20 0d |rations |on the .|
|000006c0| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|000006d0| 20 20 20 20 20 20 20 12 | 31 2e 12 30 20 20 20 20 |       .|1..0    |
|000006e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000006f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000700| 20 20 20 12 31 2e 12 30 | 20 20 11 32 2d 31 0d 0b |   .1..0|  .2-1..|
|00000710| 00 20 20 20 20 11 31 65 | 6e 74 69 72 65 20 6d 61 |.    .1e|ntire ma|
|00000720| 74 72 69 78 20 11 33 5b | 41 20 11 31 12 31 2e 12 |trix .3[|A .1.1..|
|00000730| 30 20 11 33 49 5d 11 31 | 2e 20 20 54 68 65 20 72 |0 .3I].1|.  The r|
|00000740| 65 73 75 6c 74 20 77 69 | 6c 6c 20 62 65 20 74 68 |esult wi|ll be th|
|00000750| 65 20 6d 61 74 72 69 78 | 20 11 33 5b 49 20 11 31 |e matrix| .3[I .1|
|00000760| 12 31 2e 12 30 20 11 33 | 41 20 20 5d 11 31 2e 20 |.1..0 .3|A  ].1. |
|00000770| 20 49 66 20 74 68 69 73 | 0d 0a 00 0d 0b 00 20 20 | If this|......  |
|00000780| 20 20 69 73 20 6e 6f 74 | 20 70 6f 73 73 69 62 6c |  is not| possibl|
|00000790| 65 2c 20 74 68 65 6e 20 | 11 33 41 20 11 31 69 73 |e, then |.3A .1is|
|000007a0| 20 6e 6f 74 20 69 6e 76 | 65 72 74 69 62 6c 65 2e | not inv|ertible.|
|000007b0| 0d 0a 00 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |......  |        |
|000007c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000007d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000007e0| 20 20 20 20 20 20 20 11 | 32 2d 31 20 20 20 20 20 |       .|2-1     |
|000007f0| 20 20 20 2d 31 0d 0b 00 | 20 11 31 33 2e 20 43 68 |   -1...| .13. Ch|
|00000800| 65 63 6b 20 79 6f 75 72 | 20 77 6f 72 6b 20 62 79 |eck your| work by|
|00000810| 20 6d 75 6c 74 69 70 6c | 79 69 6e 67 20 74 6f 20 | multipl|ying to |
|00000820| 73 65 65 20 74 68 61 74 | 20 11 33 41 41 20 20 20 |see that| .3AA   |
|00000830| 3d 20 49 20 3d 20 41 20 | 20 41 11 31 2e 0d 0a 00 |= I = A | A.1....|
|00000840| 53 65 63 74 69 6f 6e 20 | 31 30 2e 33 20 20 54 68 |Section |10.3  Th|
|00000850| 65 20 49 6e 76 65 72 73 | 65 20 6f 66 20 61 20 53 |e Invers|e of a S|
|00000860| 71 75 61 72 65 20 4d 61 | 74 72 69 78 0d 0b 00 46 |quare Ma|trix...F|
|00000870| 6f 72 20 73 71 75 61 72 | 65 20 73 79 73 74 65 6d |or squar|e system|
|00000880| 73 20 6f 66 20 6c 69 6e | 65 61 72 20 65 71 75 61 |s of lin|ear equa|
|00000890| 74 69 6f 6e 73 2c 20 77 | 65 20 63 61 6e 20 64 65 |tions, w|e can de|
|000008a0| 74 65 72 6d 69 6e 65 20 | 77 68 65 74 68 65 72 20 |termine |whether |
|000008b0| 74 68 65 20 12 31 73 79 | 73 74 65 6d 20 0d 0a 00 |the .1sy|stem ...|
|000008c0| 68 61 73 20 61 20 75 6e | 69 71 75 65 20 73 6f 6c |has a un|ique sol|
|000008d0| 75 74 69 6f 6e 12 30 20 | 75 73 69 6e 67 20 74 68 |ution.0 |using th|
|000008e0| 65 20 66 6f 6c 6c 6f 77 | 69 6e 67 20 72 75 6c 65 |e follow|ing rule|
|000008f0| 2e 0d 0a 00 0d 0b 00 49 | 66 20 11 33 41 20 11 31 |.......I|f .3A .1|
|00000900| 69 73 20 61 6e 20 69 6e | 76 65 72 74 69 62 6c 65 |is an in|vertible|
|00000910| 20 6d 61 74 72 69 78 2c | 20 74 68 65 6e 20 74 68 | matrix,| then th|
|00000920| 65 20 73 79 73 74 65 6d | 20 6f 66 20 6c 69 6e 65 |e system| of line|
|00000930| 61 72 20 65 71 75 61 74 | 69 6f 6e 73 20 72 65 70 |ar equat|ions rep|
|00000940| 72 65 73 65 6e 74 65 64 | 0d 0a 00 62 79 20 11 33 |resented|...by .3|
|00000950| 41 58 20 3d 20 42 20 11 | 31 68 61 73 20 61 20 75 |AX = B .|1has a u|
|00000960| 6e 69 71 75 65 20 73 6f | 6c 75 74 69 6f 6e 20 67 |nique so|lution g|
|00000970| 69 76 65 6e 20 62 79 0d | 0a 00 20 20 20 20 20 20 |iven by.|..      |
|00000980| 20 20 20 20 11 32 2d 31 | 0d 0b 00 20 20 20 20 20 |    .2-1|...     |
|00000990| 11 33 58 20 3d 20 41 20 | 20 42 11 31 2e 0d 0a 00 |.3X = A | B.1....|
|000009a0| 0d 0a 00 4e 6f 74 65 20 | 74 68 61 74 20 73 6f 6c |...Note |that sol|
|000009b0| 76 69 6e 67 20 61 20 73 | 69 6e 67 6c 65 20 73 79 |ving a s|ingle sy|
|000009c0| 73 74 65 6d 20 6f 66 20 | 6c 69 6e 65 61 72 20 65 |stem of |linear e|
|000009d0| 71 75 61 74 69 6f 6e 73 | 20 62 79 20 66 69 6e 64 |quations| by find|
|000009e0| 69 6e 67 20 74 68 65 20 | 69 6e 76 65 72 73 65 0d |ing the |inverse.|
|000009f0| 0a 00 6f 66 20 74 68 65 | 20 63 6f 65 66 66 69 63 |..of the| coeffic|
|00000a00| 69 65 6e 74 20 6d 61 74 | 72 69 78 20 69 73 20 6e |ient mat|rix is n|
|00000a10| 6f 74 20 76 65 72 79 20 | 65 66 66 69 63 69 65 6e |ot very |efficien|
|00000a20| 74 2e 20 20 48 6f 77 65 | 76 65 72 2c 20 69 66 20 |t.  Howe|ver, if |
|00000a30| 77 65 20 61 6c 72 65 61 | 64 79 20 6b 6e 6f 77 0d |we alrea|dy know.|
|00000a40| 0a 00 74 68 65 20 69 6e | 76 65 72 73 65 20 6f 66 |..the in|verse of|
|00000a50| 20 74 68 65 20 63 6f 65 | 66 66 69 63 69 65 6e 74 | the coe|fficient|
|00000a60| 20 6d 61 74 72 69 78 2c | 20 77 65 20 6b 6e 6f 77 | matrix,| we know|
|00000a70| 20 74 68 61 74 20 74 68 | 65 72 65 20 69 73 20 61 | that th|ere is a|
|00000a80| 20 75 6e 69 71 75 65 20 | 73 6f 6c 75 74 69 6f 6e | unique |solution|
|00000a90| 0d 0a 00 74 6f 20 74 68 | 65 20 63 6f 72 72 65 73 |...to th|e corres|
|00000aa0| 70 6f 6e 64 69 6e 67 20 | 73 79 73 74 65 6d 2e 20 |ponding |system. |
|00000ab0| 20 46 75 72 74 68 65 72 | 6d 6f 72 65 2c 20 69 66 | Further|more, if|
|00000ac0| 20 77 65 20 61 72 65 20 | 73 6f 6c 76 69 6e 67 20 | we are |solving |
|00000ad0| 73 65 76 65 72 61 6c 20 | 73 79 73 74 65 6d 73 0d |several |systems.|
|00000ae0| 0a 00 77 69 74 68 20 74 | 68 65 20 73 61 6d 65 20 |..with t|he same |
|00000af0| 63 6f 65 66 66 69 63 69 | 65 6e 74 20 6d 61 74 72 |coeffici|ent matr|
|00000b00| 69 78 20 28 62 75 74 20 | 64 69 66 66 65 72 65 6e |ix (but |differen|
|00000b10| 74 20 63 6f 6e 73 74 61 | 6e 74 20 74 65 72 6d 73 |t consta|nt terms|
|00000b20| 29 2c 20 69 74 20 6d 61 | 79 20 62 65 0d 0a 00 65 |), it ma|y be...e|
|00000b30| 61 73 69 65 72 20 74 6f | 20 73 6f 6c 76 65 20 65 |asier to| solve e|
|00000b40| 61 63 68 20 6f 66 20 74 | 68 65 20 73 79 73 74 65 |ach of t|he syste|
|00000b50| 6d 73 20 62 79 20 66 69 | 6e 64 69 6e 67 20 74 68 |ms by fi|nding th|
|00000b60| 65 20 69 6e 76 65 72 73 | 65 20 6a 75 73 74 20 6f |e invers|e just o|
|00000b70| 6e 63 65 2e 0d 0a 00 3c | 00 00 00 41 01 00 00 4d |nce....<|...A...M|
|00000b80| 2c 00 00 10 00 00 00 00 | 00 00 00 73 31 30 2d 33 |,.......|...s10-3|
|00000b90| 00 a9 01 00 00 7d 02 00 | 00 4d 2c 00 00 7d 01 00 |.....}..|.M,..}..|
|00000ba0| 00 00 00 00 00 73 31 30 | 2d 33 2d 31 00 52 04 00 |.....s10|-3-1.R..|
|00000bb0| 00 ee 03 00 00 4d 2c 00 | 00 26 04 00 00 00 00 00 |.....M,.|.&......|
|00000bc0| 00 73 31 30 2d 33 2d 32 | 00 6c 08 00 00 0b 03 00 |.s10-3-2|.l......|
|00000bd0| 00 4d 2c 00 00 40 08 00 | 00 00 00 00 00 73 31 30 |.M,..@..|.....s10|
|00000be0| 2d 33 2d 33 00          |                         |-3-3.   |        |
+--------+-------------------------+-------------------------+--------+--------+