Hi,I have:AX + X = B, all of them being matrices. I have the

1. Aug 9, 2011

Peter G.

Hi,

I have:

AX + X = B, all of them being matrices. I have the numbers in the A and B matrices and I have to find the exact values of a,b,c,d (numbers in the X matrix)

I wanted to check if my method is correct:

I multiplied both sides by A-1.

2X = A-1B

So my values for abcd would be half of the matrix I get when I multiply A-1 by B:

Thanks,
Peter G.

2. Aug 9, 2011

stringy

Re: Matrices

That's not quite right. We'd have

$$AX +X = (A+I)X =B,$$

so if A+I were invertible then $X = (A+I)^{-1}B$.

3. Aug 9, 2011

Staff: Mentor

Re: Matrices

To elaborate on what stringy said, here is apparently what you did:
AX + X = B
A-1AX + X = A-1B
X + X = A-1B
2X = A-1B

Step 2 above is incorrect - you didn't multiply the entire left side of the equation by A-1.

4. Aug 9, 2011

Peter G.

Re: Matrices

Hey guys,

Thanks a lot for the help. Impressive how the "Matrix World" can make me commit mistakes I probably wouldn't in the "Real Number World"

Thanks,
Peter

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