Question

If $A=\left[\begin{array}{cc}5& x\\ y& 0\end{array}\right]$ and A = A^T, then
(a) x = 0, y = 5
(b) x + y = 5
(c) x = y
(d) none of these

Answer 1

(c) x = y


$$\begin{gathered} \mathrm{Here}, \\ A=\left[\begin{array}{cc}5& x\\ y& 0\end{array}\right] \\ {A}^T=\left[\begin{array}{cc}5& y\\ x& 0\end{array}\right] \\ \mathrm{Now}, \\ A=A^T \\ \mathrm{The}\mathrm{corresponding}\mathrm{elements}\mathrm{of}\mathrm{two}\mathrm{equal}\mathrm{matrices}\mathrm{are}\mathrm{equal}. \\ \therefore \left[\begin{array}{cc}5& x\\ y& 0\end{array}\right]=\left[\begin{array}{cc}5& y\\ x& 0\end{array}\right] \\ \Rightarrow x=y \end{gathered}$$