NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.1 Question 2

Question

Evaluate (i) $\left[\begin{matrix}\cos{\left(\theta \right)} & - \sin{\left(\theta \right)}\\sin{\left(\theta \right)} & \cos{\left(\theta \right)}\end{matrix}\right]$ and (ii) $\left[\begin{matrix}x^{2} - x + 1 & x - 1\x + 1 & x + 1\end{matrix}\right]$.

Accepted Answer

Final Answer: (i) $1$; (ii) $\left(x + 1\right) \left(x^{2} - 2 x + 2\right)$ Step 1: Part 1: Step 2: For a 2×2 matrix use det A=a₁₁a₂₂−a₁₂a₂₁. Step 3: $\cos^{2}{\left(\theta \right)}$ − $- \sin^{2}{\left(\theta \right)}$ = $1$. Step 4: Part 2: Step 5: For a 2×2 matrix use det A=a₁₁a₂₂−a₁₂a₂₁. Step 6: $\left(x + 1\right) \left(x^{2} - x + 1\right)$ − $\left(x - 1\right) \left(x + 1\right)$ = $\left(x + 1\right) \left(x^{2} - 2 x + 2\right)$.

NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.1 Question 2

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