Question

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

• A. $3$
• B. $4$
• C. $2$
• D. $5$

Answer 1

The correct option is A $3$

Given, the matrix $A$ is singular.

$\Rightarrow |A|=0$

$\left|\begin{array}{ccc}8& -6& 2\\ -6& 7& -4\\ 2& -4& \lambda \end{array}\right|=0$

$8(7\lambda -16)+6(-6\lambda +8)+2\left(10\right)=0$

$\Rightarrow 20\lambda -60=0$

$\Rightarrow \lambda =3$