Question

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

• A. $5$
• B. $3$
• C. $-1$
• D. $-2$

Answer 1

The correct option is A $5$

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

Given $A^T=A$

$\Rightarrow \left[\begin{array}{cc}4& 2x-3\\ x+2& x+1\end{array}\right]=\left[\begin{array}{cc}4& x+2\\ 2x-3& x+1\end{array}\right]$

Both are equal if corresponding elements are equal

$\Rightarrow 2x-3=x+2$

$\Rightarrow 2x-x=3+2$

$\Rightarrow x=5$

Option A is correct