NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.2 Question 6

Question

Simplify $\cos{\left(\theta \right)}$ $\left[\begin{matrix}\cos{\left(\theta \right)} & \sin{\left(\theta \right)}\- \sin{\left(\theta \right)} & \cos{\left(\theta \right)}\end{matrix}\right]$ + $\sin{\left(\theta \right)}$ $\left[\begin{matrix}\sin{\left(\theta \right)} & - \cos{\left(\theta \right)}\\cos{\left(\theta \right)} & \sin{\left(\theta \right)}\end{matrix}\right]$.

Accepted Answer

Final Answer: $\left[\begin{matrix}1 & 0\0 & 1\end{matrix}\right]$ Step 1: Distribute the two scalar factors through their matrices. Step 2: The diagonal entries are cos²θ+sin²θ=1; the off-diagonal entries are cos θ sin θ−sin θ cos θ=0. Step 3: Therefore the result is I₂.

NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.2 Question 6

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