Solving Systems of DEs with Undetermined Coefficients

[Melawrghk]

Homework Statement

So I'm doing a systems of DEs question with undetermined coefficients. After comparing coefficients, I have this:
a+b=Ab+(1,0)^T

where a&b are vectors (2D) and A is the coefficient matrix:
[2 -1]
[3 -2]

I know that 'a' is (1,1)^T. I need to find b.

I tried rearranging it, but I don't know if that's right.
(1,1)-(1,0)=Ab-b
(0,1)=(A-1)b

So I found A-I:
[1 -1]
[3 -3]

I was going to invert it and multiply by (0,1), but it's not invertible. What do I do?

 

[tiny-tim]

Hi Melawrghk!

… I tried rearranging it, but I don't know if that's right.
(1,1)-(1,0)=Ab-b
(0,1)=(A-1)b

Yes, that's fine!

I tried rearranging it, but I don't know if that's right.
(1,1)-(1,0)=Ab-b
(0,1)=(A-1)b

Give up!

A - I is a projection onto the line x = y (because it sends (p,q) to (p-q,p-q)), so you can't have (A - I)b = (0,1).