# Thread: find one matrix X such that AX = B

1. ## find one matrix X such that AX = B

if
A = [1 -2 -1]
A = [2 -3 1]
A = [-3 5 0]

and
B = [0 1 0]
B = [-1 3 2]
B = [1 -4 -2]

find one matrix X such that AX = B.

A and B are 3x3 matrix above

2. $\displaystyle x=a^{-1} b.$

3. Originally Posted by Krizalid
$\displaystyle x=a^{-1}b.$
But A and B both end up with a row of zeros, they don't have an inverse.

4. B doesn't need to be invertible, just A, and A is invertible.

5. ## Invertible?

Originally Posted by Krizalid
B doesn't need to be invertible, just A, and A is invertible.
How is A invertible? Won't one find a row of zeroes on the left-hand side of the augmented matrix, implying that A is singular? Incidentally, the same situation will arise with B.

6. what's its determinant?

7. Originally Posted by Krizalid
what's its determinant?
Such that it's not invertible.

8. ohh, i just realized that i got a typo in the third row when computing the determinant.

anyway, there's no X, but at least the OP knows now how to solve the problem.

9. I have got the solution for the question,
X = [-2 3 4]
X = [-1 1 2]
X = [0 0 0 ]

thanks for the help