The matrix 0&5&-7 -5&0&11 7&-11&0 is : - Vidyadip

MCQ

The matrix $\begin{bmatrix}0&5&-7\\-5&0&11\\7&-11&0\end{bmatrix}$ is :

✓
A skew $-$ symmetric matrix.
B
A symmetric matrix.
C
A diagonal matrix.
D
An uppertriangular matrix.

✓

Answer

Correct option: A.

A skew $-$ symmetric matrix.

Here,
$\text{A}=\begin{bmatrix}0&5&-7\\-5&0&11\\7&-11&0\end{bmatrix}$
$\Rightarrow\text{A}^\text{T}=\begin{bmatrix}0&-5&7\\5&0&-11\\-7&11&0\end{bmatrix}$
$\Rightarrow\text{A}^\text{T}=-\begin{bmatrix}0&5&-7\\-5&0&11\\7&-11&0\end{bmatrix}$
$\Rightarrow\text{A}^\text{T}=-\text{A}$
Thus, $A$ is a skew $-$ symmetric matrix.

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