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

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Homework Help Overview

The discussion revolves around transitioning from the matrix equation x = Cx + d to the expression x = [(I − C)^(-1)]d. Participants are exploring the underlying concepts of matrix equations and their manipulations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Some participants question whether the transformation must be done using matrix methods or if a non-matrix approach suffices. Others suggest relating the matrix equation to a simpler algebraic form, drawing parallels to familiar numerical equations.

Discussion Status

The conversation is ongoing, with participants sharing insights and resources. Some have offered guidance on how to approach the problem, while others express uncertainty about their ability to engage with matrix concepts.

Contextual Notes

There is mention of a video resource that may provide additional context, and some participants indicate a lack of confidence in their understanding of matrices, which may influence the discussion.

Cinitiator
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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.
 
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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.
 
Cinitiator said:

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

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