Question

$A=\left[\begin{array}{cc}4& x+2\\ 2x-3& x+1\end{array}\right]$ is symmetric, then $x$ =

• A. $3$
• B. $5$
• C. $2$
• D. $4$

Answer 1

Answer: (B)

$5$

$A=\left[\begin{array}{cc}4& x+2\\ 2x-3& x+1\end{array}\right]$
$A^T=\left[\begin{array}{cc}4& 2x-3\\ x+2& x+1\end{array}\right]$
$A$ is symmetric.
$\therefore A=A^T$
$\Rightarrow 2x-3=x+2$
$\therefore x=5$
Hence, option B.