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Question
The matrix \[A = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\] is a
Options
diagonal matrix
symmetric matrix
skew-symmetric matrix
scalar matrix
Solution
Given:
\[A^T = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}^T \]
\[ = \begin{bmatrix}0 & 5 & - 8 \\ - 5 & 0 & - 12 \\ 8 & 12 & 0\end{bmatrix}\]
\[ = - 1\begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\]
\[ = - A\]
Therefore, matrix A is skew-symmetric matrix.
Hence, the correct option is (c).
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