Question

Find the inverse of the matrix $\left[\begin{array}{cc}5& 11\\ 4& 9\end{array}\right]$ by elementary transformations.

Answer 1

$A=IA\left[\begin{array}{cc}5& 11\\ 4& 9\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]A{R}_1\to R_1-R_2\left[\begin{array}{cc}1& 2\\ 4& 9\end{array}\right]=\left[\begin{array}{cc}1& -1\\ 0& 1\end{array}\right]A{R}_2\to R_2-{4R}_1\left[\begin{array}{cc}1& 2\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}1& -1\\ -4& 5\end{array}\right]A{R}_1\to R_1-{2R}_2\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}9& -11\\ -4& 5\end{array}\right]A\therefore A^{-1}=\left[\begin{array}{cc}9& -11\\ -4& 5\end{array}\right]$