NCERT Class 12 · Ch 3 Exercise 3.3 · Q12

NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.3 Question 12

For A=\(\left[\begin{matrix}\cos{\left(\alpha \right)} & - \sin{\left(\alpha \right)}\\\sin{\left(\alpha \right)} & \cos{\left(\alpha \right)}\end{matrix}\right]\) and A+Aᵀ=I, choose the listed value of α.

(A) π/6
(B) π/3
(C) π
(D) 3π/2

💡 Concept Hints

Check the matrix orders and the meaning of the requested operation before calculating.
Keep row and column indices in order. Compare corresponding entries only after the matrix expressions have compatible dimensions.

✅ Step-by-Step Solution

Final Answer: B: π/3.

Adding the matrix and its transpose cancels off-diagonal terms and gives 2cos α I.
Thus 2cos α=1. The real solutions are α=2kπ±π/3, k∈ℤ; among the listed options π/3 satisfies this.

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NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.3 Question 12

💡 Concept Hints

✅ Step-by-Step Solution

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