Question

If the matrix $A=\left[\begin{array}{ccc}8& -6& 2\\ -6& 7& -4\\ 2& -4& \lambda \end{array}\right]$ is singular one, then $\lambda$ is:

• A. $3$
• B. $4$
• C. $2$
• D. $5$

Answer 1

The correct option is A $3$

(A) For singular matrix deteminant of A =0

$\left|\begin{array}{ccc}8& -6& 2\\ -6& 7& -4\\ 2& -4& \lambda \end{array}\right|=0$
$\Rightarrow 2\left|\begin{array}{cc}-6& 2\\ 7& -4\end{array}\right|+4\left|\begin{array}{cc}8& 2\\ -6& -4\end{array}\right|+\lambda \left|\begin{array}{cc}8& -6\\ -6& 7\end{array}\right|=0$
$\Rightarrow 2(24-14)+4(-32+12)+\lambda (56-36)=0$
$\Rightarrow 20-80+20\lambda =0$
$\Rightarrow \lambda =3$