Question

If the inverse of the matrix $\left[\begin{array}{ccc}\alpha & 14& -1\\ 2& 3& 1\\ 6& 2& 3\end{array}\right]$ does not exist then the value of $\alpha$ is

• A. 1
• B. -1
• C. 0
• D. -2

Answer 1

Answer: (D)

$A=\left[\begin{array}{ccc}\alpha & 14& -1\\ 2& 3& 1\\ 6& 2& 3\end{array}\right]$
$|A|=\alpha [9-2]-14[6-6]-1[4-18]$
$|A|=7\alpha +14$
$A^{-1}$ does not exists if $|A|=0$
$\Rightarrow 7\alpha +14=0$
$\Rightarrow \alpha =-2$