Class 12 Matrices · Conceptual Answer1 Markstranspose_operations
Class 12 Maths · Matrices · Conceptual Answer #42
For A=\(\begin{bmatrix}\cos\theta & -\sin\theta\\\sin\theta & \cos\theta\end{bmatrix}\), find AAᵀ.
✅ Step-by-Step Solution
Final Answer: \(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)
- Multiplication gives diagonal entries cos²θ+sin²θ=1 and off-diagonal entries cosθsinθ−sinθcosθ=0.
- \(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Multiplication gives diagonal entries cos²θ+sin²θ=1 and off-diagonal entries cosθsinθ−sinθcosθ=0.
- [0.5 marks] \(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)
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