Question

If the matrix $A=\left[\begin{array}{ccc}5& 2& x\\ y& 2& -3\\ 4& t& -7\end{array}\right]$ is a symmetric matrix, then find the value of $x,y$ and $t$ respectively,

• A. $4,2,3$
• B. $4,2,-3$
• C. $4,2,-7$
• D. $2,4,-7$

Answer 1

Answer: (B)

$A$ is a symmetric matrix $\therefore A=A^T$
$\Rightarrow \left[\begin{array}{ccc}5& 2& x\\ y& 2& -3\\ 4& t& -7\end{array}\right]=\left[\begin{array}{ccc}5& y& 4\\ 2& 2& t\\ x& -3& -7\end{array}\right]$
On comparing, we get
$\Rightarrow y=2,x=4,t=-3$