NCERT Class 12 · Ch 4 Miscellaneous Exercise · Q9

NCERT Class 12 Maths · Chapter 4 Determinants · Miscellaneous Exercise Question 9

If A=\(\left[\begin{matrix}1 & \sin{\left(\theta \right)} & 1\\- \sin{\left(\theta \right)} & 1 & \sin{\left(\theta \right)}\\-1 & - \sin{\left(\theta \right)} & 1\end{matrix}\right]\) and 0≤θ≤2π, find the range of |A|.

(A) 0
(B) (2,∞)
(C) (2,4)
(D) [2,4]

💡 Concept Hints

Identify whether this needs determinant expansion, an inverse, or the absolute determinant formula for area.
For a determinant use signed cofactors. For a system first check invertibility; for an area take half the absolute determinant.

✅ Step-by-Step Solution

Final Answer: D: [2,4].

Expanding the determinant gives \(2 \sin^{2}{\left(\theta \right)} + 2\).
Because 0≤sin²θ≤1, we obtain 2≤det A≤4.
Both endpoints are attained: θ=0 gives 2 and θ=π/2 gives 4. Continuity gives every intermediate value.

Master Chapter 4: Determinants

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Determinants.

📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →

← Previous Question

For A=diag(x,y,z), where xyz≠0, find A⁻¹.

All Questions in Determinants — Miscellaneous Exercise

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9

NCERT Class 12 Maths · Chapter 4 Determinants · Miscellaneous Exercise Question 9

💡 Concept Hints

✅ Step-by-Step Solution

Master Chapter 4: Determinants

All Questions in Determinants — Miscellaneous Exercise

Related Questions in Determinants