Question

Let $A$ and $B$ are two matrices of same order $3\times 3$ given by

$A=\left[\begin{array}{ccc}1& 3& \lambda +2\\ 2& 4& 6\\ 3& 5& 8\end{array}\right],$ $B=\left[\begin{array}{ccc}3& 2& 4\\ 3& 2& 5\\ 2& 1& 4\end{array}\right]$

If $A$ is a singular matrix, then $tr(A+B)$ is equal to

• A. $24$
• B. $11$
• C. $22$
• D. None of these

Answer 1

The correct option is C $22$

Given, $A=\left[\begin{array}{ccc}1& 3& \lambda +2\\ 2& 4& 6\\ 3& 5& 8\end{array}\right],B=\left[\begin{array}{ccc}3& 2& 4\\ 3& 2& 5\\ 2& 1& 4\end{array}\right]$
$A+B=\left[\begin{array}{ccc}4& 5& \lambda +6\\ 5& 6& 11\\ 5& 6& 12\end{array}\right]$
$tr(A+B)=4+6+12=22$