Question

lf $A$ is $\left\{\begin{array}{ccc}8& -6& 2\\ -6& 7& -4\\ 2& -4& \lambda \end{array}\right\}$ is a singular matrix then $\lambda =$

• A. 3
• B. 4
• C. 2
• D. 5

Answer 1

The correct option is A 3

Given, $A=\left(\begin{array}{ccc}8& -6& 2\\ -6& 7& -4\\ 2& -4& \lambda \end{array}\right)$ is a singular matrix
So, det A=0
$\therefore$ BY operation of matrix (s),
$detA=8(7\lambda -16)+6[-6\lambda +8]+2[24-14]$
$=56\lambda -128-36\lambda +48+20$
$=20\lambda -60$
So, $detA=0=20\lambda -60$
$\lambda =3$