hello,
Can someone please help me with this problem?
(I+2A)^-1 = [ -1 2 ]
[ 4 5 ]
not sure how to make a matrix...
it's suppose to be a 2 x 2 matrix with row 1 = -1, 2 and row 2 = 4, 5
Thanks!
$\displaystyle (I+2A)^{-1}=\begin{pmatrix}\!\!-1&2\\4&5\end{pmatrix}\Longleftrightarrow I+2A=\begin{pmatrix}\!\!-1&2\\4&5\end{pmatrix}^{-1}=\begin{pmatrix}\!\!-5/13&2/13\\4/13&1/13\end{pmatrix}\Longleftrightarrow$
$\displaystyle 2A=\begin{pmatrix}\!\!-18/13&2/13\\4/13&\!\!-12/13\end{pmatrix}$ ...and now divide by 2 and find your matrix.
Note that at the end you must check that $\displaystyle I+2A$ is actually invertible, otherwise the problem's no solution.
Tonio