Solving Matrix Equations: x = Cx + d to x = [(I - C)^(-1)]d

[Cinitiator]

Homework Statement

How does one go from

x = Cx + d

to

x = [(I − C)^(-1)]d

in a matrix equation?

Homework Equations

x = Cx + d

x = [(I − C)^(-1)]d

The Attempt at a Solution

I tried to Google.

 

[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.

 

[Dick]

Homework Statement

How does one go from

x = Cx + d

to

x = [(I − C)^(-1)]d

in a matrix equation?

Homework Equations

x = Cx + d

x = [(I − C)^(-1)]d

The Attempt at a Solution

I tried to Google.

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

 

[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'?

 

[Mark44]

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.

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

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