- #1

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Is there algorithm to find such matrix of n*n?

Thanks.

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- Thread starter posuchmex
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If the determinant doesn't change, you've found the inverse!In summary, the inverse of a matrix with integer entries can be found if and only if its determinant is 1.f

- #1

- 5

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Is there algorithm to find such matrix of n*n?

Thanks.

- #2

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any ideas please?

- #3

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Both matrices will probably contain only zeros and ones.

- #4

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our teacher said there are some without zeros

- #5

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Use only 1's and 0's for simplicity. Anyway I suspect that any other example will be a multiple or something simply related to such a matrix.

Instead of thinking about 4X4 matrices yet, attack a simpler case - 2X2 matrices. You can surely find several 2X2 matrices that have your property.

Then does that suggest a plan for extending to construction of suitable 3X3 matrices? If you can do that you will probably be able to do it for 4X4 too.

- #6

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- #7

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Both matrices will probably contain only zeros and ones.

not so:

[1 1][2 -1]...[1 0]

[1 2][-1 1] = [0 1]

- #8

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Halls of Ivy: isn't this true for matrices with determinant ± 1?

Last edited:

- #9

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i can't find 4x4 this matrix

can you show me one please

can you show me one please

Last edited:

- #10

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i can't find 4x4 this matrix

can you show me one please

Can you find a 4x4 matrix with integer entries whose determinant is 1??

- #11

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Where did you leave it last? Retrace your steps, and you may find it... or:

Start with the 4x4 identity, and apply transformations to the rows that preserve the value of

the determinant.

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