Question

Find the inverse of the following matrices:
(a) $\left[\begin{array}{ccc}1& 4& 0\\ -1& 2& 2\\ 0& 0& 2\end{array}\right]$
(b)$\left[\begin{array}{ccc}cos\theta & -sin\theta & 0\\ sin\theta & cos\theta & 0\\ 0& 0& 1\end{array}\right]$
(c) $\left[\begin{array}{ccc}2& 2& 2\\ 2& 5& 5\\ 2& 5& 11\end{array}\right]$
(d) $\left[\begin{array}{ccc}1& 2& 3\\ 2& 4& 5\\ 3& 5& 6\end{array}\right]$
(e) $\left[\begin{array}{ccc}1& 4& 0\\ -1& 2& 2\\ 0& 0& 2\end{array}\right]$

Answer 1

(a) $A^{-1}=-\frac{1}{58}\left[\begin{array}{ccc}-11& -9& 1\\ 4& -2& -3\\ 10& -5& 7\end{array}\right]$
(b)$A^{-1}=\left[\begin{array}{ccc}cos\theta & sin\theta & 0\\ sin\theta & cos\theta & 0\\ 0& 0& 1\end{array}\right]$
(c) $A^{-1}=\frac{1}{6}\left[\begin{array}{ccc}5& -2& 0\\ -2& 3& -1\\ 0& -1& 1\end{array}\right]$
(d) $A^{-1}=\left[\begin{array}{ccc}1& -3& 3\\ -3& 3& -1\\ 2& -1& 0\end{array}\right]$
(e) $A^{-1}=\frac{1}{6}\left[\begin{array}{ccc}2& -4& 4\\ 1& 1& -1\\ 0& 0& 3\end{array}\right]$