Question

A=-3 1 1
| 1 -3 1|
 1 1 -3
Calculate A(A+5I) and use the result to find the inverse of A.

Answer 1

I got: -4 0 0
| 0 -4 0|
 0 0 -4
for the computation. And I got:
-1/4 0 0
| 0 -1/4 0|
 0 0 -1/4 for the inverse. Is this the correct inverse?

Answer 2

I'm getting
\[\Large A(A+5I) = \begin{bmatrix}-4 & 0 & 0\\0 & -4 & 0\\0 & 0 & -4\\ \end{bmatrix}\] as well

Answer 3

I don't agree with your inverse though. I'm getting a different matrix for \(\Large A^{-1}\)

Answer 4

To check, the product of \(\Large A\) and \(\Large A^{-1}\) (in either order) should be equal to \[\Large I_3 = \begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\]

Answer 5

@jim_thompson5910
I did the inverse of the computation. I also did the inverse of just A and got:
\[\left[\begin{matrix}-1/2 & -1/4 & -1/4 \\ -1/4 & -1/2 & -1/4 \\ -1/4 & -1/4 & -1/2\end{matrix}\right]\] I did the product of \[A \ and\ A^-1\] and got the \[I_3\] matrix.

Answer 6

You have the correct inverse

Answer 7

I'm not sure how `Calculate A(A+5I) and use the result to find the inverse of A.` fits into finding the inverse of A though

Answer 8

@jim_thompson5910 Thanks for the help!
I'm not sure either, maybe its just worded wrong.

Answer 9

you're welcome