Matrix A where system Ax = b solvable, but not nec. uniquely  TOPIC_SOLVED

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Matrix A where system Ax = b solvable, but not nec. uniquely

Postby testing on Wed Mar 04, 2009 7:41 pm

Give an example of a matrix A for which the system Ax= b can be solved for any b, but not necessarily uniquely.

Is there a way to do this that does not involve "brute force"?
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Postby stapel_eliz on Tue Mar 10, 2009 1:50 pm

testing wrote:Give an example of a matrix A for which the system Ax= b can be solved for any b, but not necessarily uniquely.

Is there a way to do this that does not involve "brute force"?

Maybe, but I'm not seeing it. :oops:

In any case, "brute force" isn't too bad here, since you can pick the matrix to be any size you like. So let A, x, and b be the following system:

[ a  b ][x]   [s]
[ c d ][y] = [t]

This system will be dependent (and thus not uniquely solvable) if the second row is a multiple of the first, so you can pick anything you like for the first row, and then make the second a muliple of it. :wink:
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