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# Linear Algebra Foundations #6 - An Equation involving Matrices

# Linear Algebra Foundations #6 - An Equation involving Matrices

sonofhotmale + 0 comments Yikes, I was solving this question as if x,y were vectors. I was getting completely stuck until I reread the problem and found that X and Y are integers. Then everything clicked. Got the same answers as below

tpepin96 + 0 comments My approach was to find A^2, leaving you with one linear equation for each of the nine cells.

Most of them are repeats; for the zero cells, you get five:

`0 + 0x + 0y = 0`

You also have this equation three times, along the diagonals:

`1 + x + y = 0`

And finally this equation, for the top-middle cell:

`2 + x = 0`

Which yields the solution that others have said below. My question is, is there a more systematic way of solving this?

toby_shearman + 0 comments There is a nice trick here in decomposing A as the identity plus a nilpotent matrix (or degree or order 2).

GHacked + 0 comments -2 1

GHacked + 0 comments -2 1

ktulu315 + 0 comments X = -2, Y = 1.

Explanation: Giving 2 ecuations:

1 + x + y = 0; <<< 1 2 + x = 0; <<< 2

clearing x in 2:

x = -2; <<< 3

replacing 3 in 1:

1 - 2 + y = 0;

clearing y:

y = 2 -1; y = 1;

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