Matrices
NCERT Class 12
CBSE
Grade 12
Question:
If $A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix}$, verify that $(A - A')$ is a skew-symmetric matrix.
Step-by-Step Solution
$C = A - A' = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$. [1.0 Mark]
$C' = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} = -C \Rightarrow (A - A')$ is skew-symmetric. Proved! [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Calculating difference matrix $A - A'$: 1.0 Mark
Verifying transpose equals negative difference: 1.0 Mark
Correct Answer:
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