Question

$IfA=\left[\begin{array}{ccc}2& x-3& x-2\\ 3& -2& -1\\ 4& -1& -5\end{array}\right]$ is a symmetric matrix then $x$

• A. $0$
• B. $3$
• C. $6$
• D. $8$

Answer 1

The correct option is C $6$

Given $A=\left[\begin{array}{ccc}2& x-3& x-2\\ 3& -2& -1\\ 4& -1& -5\end{array}\right]$ is a symmetric matrix.
So, by property of symmetric matrices
$A=A^T$
$\Rightarrow \left[\begin{array}{ccc}2& x-3& x-2\\ 3& -2& -1\\ 4& -1& -5\end{array}\right]=\left[\begin{array}{ccc}2& 3& 4\\ x-3& -2& -1\\ x-2& -1& -5\end{array}\right]$
So, By operation of matrices - equality,
$\Rightarrow x-3=3$
$\Rightarrow x=6$