Class 12 Matrices · Long Answer3 Markstranspose_operations
Class 12 Maths · Matrices · Long Answer #65
For A=\(\begin{bmatrix}1\\-4\\3\end{bmatrix}\) and B=\(\begin{bmatrix}-1 & 2 & 1\end{bmatrix}\), verify (AB)ᵀ=BᵀAᵀ.
✅ Step-by-Step Solution
Final Answer: \(\begin{bmatrix}-1 & 4 & -3\\2 & -8 & 6\\1 & -4 & 3\end{bmatrix}\)
- Compute the outer product AB=[[-1,2,1],[4,−8,−4],[−3,6,3]].
- Transposing gives (AB)ᵀ=[[-1,4,−3],[2,−8,6],[1,−4,3]].
- Independently BᵀAᵀ=[[-1],[2],[1]][1,−4,3]=[[-1,4,−3],[2,−8,6],[1,−4,3]].
- The two matrices agree, verifying (AB)ᵀ=BᵀAᵀ.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Compute the outer product AB=[[-1,2,1],[4,−8,−4],[−3,6,3]].
- [1 mark] Transposing gives (AB)ᵀ=[[-1,4,−3],[2,−8,6],[1,−4,3]].
- [1 mark] Independently BᵀAᵀ=[[-1],[2],[1]][1,−4,3]=[[-1,4,−3],[2,−8,6],[1,−4,3]].
- [0.5 marks] The two matrices agree, verifying (AB)ᵀ=BᵀAᵀ.
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