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प्रश्न
उत्तर
\[Given: \hspace{0.167em} A = \begin{bmatrix}5 & 2 & x \\ y & z & - 3 \\ 4 & t & - 7\end{bmatrix}\]
\[ \Rightarrow A^T = \begin{bmatrix}5 & y & 4 \\ 2 & z & t \\ x & - 3 & - 7\end{bmatrix}\]
Since A is a symmetric matrix,`( A^T)` = A .
\[ \Rightarrow \begin{bmatrix}5 & y & 4 \\ 2 & z & t \\ x & - 3 & - 7\end{bmatrix} = \begin{bmatrix}5 & 2 & x \\ y & z & - 3 \\ 4 & t & - 7\end{bmatrix}\]
The corresponding elements of two equal matrices are equal .
\[ \therefore x = 4 \]
\[ y = 2 \]
\[ z = z \]
\[ t = - 3\]
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