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proj08.pro
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1989-05-25
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PROJECT 8.
Consider the following sequence of matrices:
┌ ┐ ┌ ┐ ┌ ┐
│ 1 2 │ │ 1 2 3 │ │ 1 2 3 4 │
│ 3 4 │ , │ 4 5 6 │ , │ 5 6 7 8 │ , etc.
└ ┘ │ 7 8 9 │ │ 9 10 11 12 │
└ ┘ │ 13 14 15 16 │
└ ┘
Try to calculate their inverses; make a conjecture. Note that their rows are all in arithmetic progression. Can you make a more general conjecture? What can you prove?