System of Equations

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• Feb 6th 2013, 01:00 PM
Launcher
System of Equations
I need to find out how to solve a system of equations with the given matrix form:

AX=CX+B;

I know I need to make it in the form of X= with inverse of A and C as well as using the identity matrix

What I have guessed at the moment is
X= (I-A)^-1 + (I-C)^-1 + B

I am using excel as I have an equation I have to solve with this but if I can figure out the formula for this I can solve the problem fairly easy.

Thanks!
• Feb 6th 2013, 01:16 PM
chiro
Re: System of Equations
Hey Launcher.

Re-arranging we get AX - CX = B which implies (A-C)X = B which implies X = (A-C)^(-1)*B.
• Feb 6th 2013, 01:26 PM
Launcher
Re: System of Equations
Oh wow thanks! I knew I had to re arrange them one way or another but on my other examples I have had to use the Identity matrix in with my equation to solve the problem. However, X= (A-C)(-1)*B looks like it may do the trick as well! I will try this out in excel with my given equation now and see what I come up with!

This is the equation I am trying to solve for X which is teh x,y,z,w matrix.

http://i.imgur.com/wkvGTCJ.png
• Feb 6th 2013, 02:14 PM
Launcher
Re: System of Equations
By using excel I got:

x=-5
y=-10
z=5
w=10

Does this look correct?
• Feb 6th 2013, 02:20 PM
chiro
Re: System of Equations
Try substituting your X vector back in and see if it checks out.
• Feb 6th 2013, 02:29 PM
Launcher
Re: System of Equations
Yes looks like it checks out! I just wanted to make sure =]
Thanks for all your help chiro your amazing