The matrix [ lll 1 & 0 & 0 0 & 2 & 0 0 & 0 & 4 ] is a: - Vidyadip

MCQ

The matrix $\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{array}\right]$ is a:

A
identity matrix
✓
symmetric matrix
C
skew-symmetric matrix
D
None of these

✓

Answer

Correct option: B.

symmetric matrix

(B) symmetric matrix
Explanation :
$\begin{aligned}A & =\left[\begin{array}{lll}1 & 0 & 0 \\0 & 2 & 0 \\0 & 0 & 4\end{array}\right] \\\therefore A^{\prime} & =\left[\begin{array}{lll}1 & 0 & 0 \\0 & 2 & 0 \\0 & 0 & 4\end{array}\right]=A\end{aligned}$
So, the given matrix is a symmetric matrix.
[Since, in a square matrix $A$, if $A^{\prime}=A$, then $A$ is called symmetric matrix.]

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