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Question
If \[A = \begin{bmatrix}5 & x \\ y & 0\end{bmatrix}\] and A = AT, then
Options
x = 0, y = 5
x + y = 5
x = y
none of these
Solution
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 .
\[ \therefore \begin{bmatrix}5 & x \\ y & 0\end{bmatrix} = \begin{bmatrix}5 & y \\ x & 0\end{bmatrix}\]
\[ \Rightarrow x = y\]
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