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.
The equation uses matrices, so if you don't feel confident answering a question that involves matrices, you shouldn't respond.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.
Shootertrex said:edit:
http://www.youtube.com/watch?v=tuepwWQ4_mM I think you might find this helpful.
A matrix equation is an equation that involves matrices, which are rectangular arrays of numbers. It is expressed in the form of Ax = b, where A is the coefficient matrix, x is the variable matrix, and b is the constant matrix.
The purpose of solving matrix equations is to find the unique solution for the variable matrix x that satisfies the equation Ax = b. This is useful in many fields, such as engineering, physics, and economics, where systems of linear equations often arise.
In a regular equation, the operations involve only numbers, while in a matrix equation, the operations involve matrices. This means that in a matrix equation, the variables can be arrays of numbers rather than just single numbers.
The inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix. It is denoted as A-1 and is only defined for square matrices.
To solve a matrix equation of the form x = Cx + d using the formula x = [(I - C)^(-1)]d, you first need to find the inverse of (I - C). Then, multiply this inverse by d to get the solution for x. This formula is based on the idea that when you subtract Cx from both sides of the equation, you get x - Cx = d, which can be rewritten as (I - C)x = d.