# Matrix equation

1. Feb 15, 2012

### Cinitiator

1. The problem statement, all variables and given/known data
How does one go from

x = Cx + d

to

x = [(I − C)^(-1)]d

in a matrix equation?

2. Relevant equations
x = Cx + d

x = [(I − C)^(-1)]d

3. The attempt at a solution
I tried to Google.

2. Feb 15, 2012

### Shootertrex

Do you need to get there using a matrix equation or just know how to get there? I know how to get to that equation without matrices. I would not know how to get there with them though. Matrices were never my strong suit.

edit:
http://www.youtube.com/watch?v=tuepwWQ4_mM I think you might find this helpful.

3. Feb 15, 2012

### Dick

I is the identity matrix, yes? Ix=x. So write the equation as Ix=Cx+d. Can you take it from there?

4. Feb 15, 2012

### genericusrnme

Think about how you'd solve this with your usual numbers
x=ax+b
(1-a)x=b
x=(1-a)^-1 b
You followin'?

5. Feb 15, 2012

### Staff: Mentor

The equation uses matrices, so if you don't feel confident answering a question that involves matrices, you shouldn't respond.