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Class 12 Matrices · Conceptual Answer1 Marksmatrix_linear_combinations

Class 12 Maths · Matrices · Conceptual Answer #38

Simplify cosθ \(\begin{bmatrix}\cos\theta & \sin\theta\\-\sin\theta & \cos\theta\end{bmatrix}\) + sinθ \(\begin{bmatrix}\sin\theta & -\cos\theta\\\cos\theta & \sin\theta\end{bmatrix}\).

✅ Step-by-Step Solution

Final Answer: \(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)
  1. The diagonal entries become cos²θ+sin²θ=1; the off-diagonal terms cancel as sinθcosθ−sinθcosθ=0.
  2. \(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] The diagonal entries become cos²θ+sin²θ=1; the off-diagonal terms cancel as sinθcosθ−sinθcosθ=0.
  • [0.5 marks] \(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)

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