Discussion Forum

If the  inverse of the matrix $\begin{bmatrix}\alpha & 14&-1 \\2 & 3&1\\6&2&3\end{bmatrix}$  does not exist, then the value of $\alpha$ is 

Answer:

Explanation:

Let A= $\begin{bmatrix}\alpha & 14&-1 \\2 & 3&1\\6&2&3\end{bmatrix}$

$\Rightarrow$    |A|= $\begin{bmatrix}\alpha & 14&-1 \\2 & 3&1\\6&2&3\end{bmatrix}$=

$=\alpha(9-2)-14(6-6)-1(4-18)= 7\alpha-0+1 \times14$

|A|= 7$\alpha$+14

It is given that inverse of A does not exists

$\therefore$   |A|=0

$\Rightarrow$      7$\alpha$+14=0

$\Rightarrow$   $\alpha$ =-2