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Question
The matrix \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\] is
Options
identity matrix
symmetric matrix
skew-symmetric matrix
diagonal matrix
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Solution
Given:
\[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\]
\[A^T = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}^T \]
\[ = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\]
\[ = A\]
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