Question

If \[A = \begin{bmatrix}5 & x \\ y & 0\end{bmatrix}\]  and A = A^T, then

Options

• x = 0, y = 5

•  x + y = 5

•  x = y 

• none of these

Answer 1

x = y 

\[Here, \]

\[A = \begin{bmatrix}5 & x \\ y & 0\end{bmatrix} \]

\[ A^T = \begin{bmatrix}5 & y \\ x & 0\end{bmatrix}\]

\[Now, \]

\[A = A^T \]

The corresponding elements of two equal matrices are equal .

\[ \therefore \begin{bmatrix}5 & x \\ y & 0\end{bmatrix} = \begin{bmatrix}5 & y \\ x & 0\end{bmatrix}\]

\[ \Rightarrow x = y\]