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GATE 2024 MN – Question 38

Engineering Mathematics · Linear Algebra · 2 marks · Multiple choice

Given $A=\begin{pmatrix}1&4&3\\5&2&1\\6&4&3\end{pmatrix}$, classify $B=A-A^T$.

  1. Symmetric
  2. Skew symmetric
  3. Diagonal
  4. Scalar

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Show answer and explanation

Correct answer: (B) Skew symmetric

Explanation

Transpose B to obtain Bᵀ=Aᵀ−A=−B. This is exactly the defining property of skew symmetry, so B. The diagonal entries are zero, but nonzero off-diagonal differences prevent the matrix from being a diagonal or scalar matrix.

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