The matrix $A = \begin{bmatrix} \sqrt{5} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{5} \end{bmatrix}$ is an:
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- symmetric matrix
- identity matrix
- null matrix
- scalar matrix
The Correct Option is A
Solution and Explanation
A scalar matrix is a diagonal matrix in which all the diagonal elements are equal. In this case, the matrix has the diagonal elements $\sqrt{5}$, $\sqrt{2}$, and $\sqrt{5}$, which are not equal. Therefore, this is not a scalar matrix. However, it is a diagonal matrix and the definition of a scalar matrix requires all diagonal elements to be the same.
So, this is not a scalar matrix, making it a symmetric matrix as it satisfies $A = A^T$ for this case. The correct answer is (A).
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