Question

If the matrix $\left[\begin{array}{ccc}\alpha & 2& 2\\ -3& 0& 4\\ 1& -1& 1\end{array}\right]$ is not invertible, then:

• A. $\alpha =-5$
• B. $\alpha =5$
• C. $\alpha =-0$
• D. $\alpha =-1$

Answer 1

The correct option is A $\alpha =-5$

For a matrix to be not invertible, determinant of the matrix should be $0$
So, $\left|\begin{array}{ccc}\alpha & 2& 2\\ -3& 0& 4\\ 1& -1& 1\end{array}\right|=0$

$\Rightarrow -(-3)(2-(-2\left)\right)-4(-\alpha -2)=0\Rightarrow 12+4\alpha +8=0\Rightarrow 4\alpha =-20\Rightarrow \alpha =-5$
Hence, option A is correct