Class 12 Matrices · Short Answer2 Markssymmetric_and_skew_symmetric
Class 12 Maths · Matrices · Short Answer #56
For A=\(\begin{bmatrix}2 & 3\\5 & 7\end{bmatrix}\), find A+Aᵀ and verify it is symmetric.
✅ Step-by-Step Solution
Final Answer: \(\begin{bmatrix}4 & 8\\8 & 14\end{bmatrix}\)
- Transpose A to obtain Aᵀ=[[2,5],[3,7]].
- Add corresponding entries: A+Aᵀ=[[4,8],[8,14]]. Its transpose is the same matrix.
- Therefore A+Aᵀ=\(\begin{bmatrix}4 & 8\\8 & 14\end{bmatrix}\) is symmetric.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Transpose A to obtain Aᵀ=[[2,5],[3,7]].
- [1 mark] Add corresponding entries: A+Aᵀ=[[4,8],[8,14]]. Its transpose is the same matrix.
- [0.5 marks] Therefore A+Aᵀ=\(\begin{bmatrix}4 & 8\\8 & 14\end{bmatrix}\) is symmetric.
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