Question

Find A^-1 in terms of A, where A^2-5A+2I=0.

Answer 1

well, if \[A=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]
then \[A^{-1}=\frac{2a}{-b\pm\sqrt{b^2-4ac}}\]
???

Answer 2

These are matrices

Answer 3

oh. K then
\[
A(A-5)=-2I\\
\text{premultiplying with A^{-1}}\\
A^{-1}A(A-5)=-2A^{-1}I\\
A-5=-2A^{-1}\\
A^{-1}={1\over2}(A-5)
\]

Answer 4

@electrokid How do you subtract a matrix with a scalar?

Answer 5

oh yea..
\[A^{-1}={1\over2}(A-5I)\]

Answer 6

Does \(5A = A5I\)?

Answer 7

interesting.

Answer 8

I definitely need to brush up on my linear algebra.

Answer 9

yes..