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Question
The matrix \[\begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\] is
Options
a skew-symmetric matrix
a symmetric matrix
a diagonal matrix
an uppertriangular matrix
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Solution
a skew-symmetric matrix
Here,
A =
\[\begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\]
\[\Rightarrow\]AT =
\[\begin{bmatrix}0 & - 5 & 7 \\ 5 & 0 & - 11 \\ - 7 & 11 & 0\end{bmatrix}\]
\[\Rightarrow A^T = - \begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\]
\[ \Rightarrow A^T = - A\]
Thus, A is a skew-symmetric matrix.
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