Question

Find the inverse of the following matrice by elementary transformation :
$\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 4\\ 3& 4& 5\end{array}\right]$

Answer 1

$A=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 4\\ 3& 4& 5\end{array}\right]$

$|A|=1(15-16)-2(10-12)+3(8-9)=-1+4-3=0$

Hence, the inverse of the given matrix does not exist.