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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
The matrix $\text{A}=\begin{bmatrix}0&-5&8\\5&0&12\\-8&-12&0\end{bmatrix}$ is a :
  • A
    Diagonal matrix.
  • B
    Symmetric matrix.
  • ✓
    Skew $-$ symmetric matrix.
  • D
    Scalar matrix.
✓

Answer

Correct option: C.
Skew $-$ symmetric matrix.
Given $\text{A}=\begin{bmatrix}0&-5&8\\5&0&12\\-8&-12&0\end{bmatrix}$
$\text{A}^\text{T}=\begin{bmatrix}0&5&-8\\-5&0&-12\\8&12&0\end{bmatrix}$
$\Rightarrow\text{A}=-\text{A}^\text{T}$
So, $A$ is skew $-$ symmetric matrix.

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