Question

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

• A. $0$
• B. $3$
• C. $6$
• D. $8$

Answer 1

Answer: (C)

$6$

If $A$ is a symmetric matrix then $a_{ij}=a_{ji}$

i.e. $a_{12}=a_{21}$ and $a_{13}=a_{31}$

$\therefore x-3=3$ and $x-2=4$

adding both we get$2x-5=7$

$\Rightarrow 2x=12\Rightarrow x=6$