- #1
BraedenP
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Homework Statement
[tex](C-CB)^{-1}=B^{-1}E[/tex]
Solve the system for B, with the assumption that C,B, and (C-CB) are invertible.
Homework Equations
The rules for matrix invertibility (but I've already come to the conclusion that all matrices in this equation are invertible.
The Attempt at a Solution
I attempted to get a solution, but I don't think it's correct:
First I applied the inversion to everything inside the function:
[tex]C^{-1}-C^{-1}B^{-1}=B^{-1}E[/tex]
Then I multiplied both sides by E, to cancel out the inverse on the right side:
[tex]C^{-1}B-C^{-1}=E[/tex]
Then I moved the [tex]C^{-1}[/tex] term to the right-hand side:
[tex]C^{-1}B=E+C^{-1}[/tex]
Finally, I multiplied both sides by [tex]C^{-1}[/tex] to isolate X:
[tex]B=CE[/tex]
This is the solution I got to, but it doesn't seem right. Have I missed anything, made an error in an assumption or calculation, or have I taken a completely wrong direction?
Any help would be greatly appreciated!
Thanks,
Braeden