What is the value of the determinant

Question

Question

This question was previously asked in

NDA (Held On: 23 April 2017) Maths Previous Year paper

Attempt in App

Answer 1

Concept:

If then determinant of A is given by:

|A| = a₁₁ × {(a₂₂ × a₃₃) – (a₂₃ × a₃₂)} - a₁₂ × {(a₂₁ × a₃₃) – (a₂₃ × a₃₁)} + a₁₃ × {(a₂₁ × a₃₂) – (a₂₂ × a₃₁)}
Elementary row or column transformations do not change the value of the determinant of a matrix.

Calculation:

Given:

Apply R₂→ R₂ – R₁ and R₃→ R₃ – R₁, we get

Expanding along R₁, we get

Δ = 1 (x²y²z² – 0) – 0 + 0

∴ Δ = x²y²z²