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Find the value of determinant. (i) {vmatrix} & - & {vm

Question

Find the value of determinant.
(i) $∣ ∣ cos θ sin θ - sin θ cos θ ∣ ∣$
(ii) $∣ ∣ x^{2} - x + 1 x + 1 x - 1 x + 1 ∣ ∣$

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Michael Discussed

Find the value of determinant.
(i)

∣ ∣ cos θ sin θ - sin θ cos θ ∣ ∣

(ii)

∣ ∣ x^{2} - x + 1 x + 1 x - 1 x + 1 ∣ ∣

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Text solutionVerified

(i)

∣ ∣ cos θ sin θ - sin θ cos θ ∣ ∣

= (cos θ) (cos θ) - (- sin θ) (sin θ) = cos^{2} θ + sin^{2} θ = 1

(ii)

∣ ∣ x^{2} - x + 1 x + 1 x - 1 x + 1 ∣ ∣

= (x^{2} - x + 1) (x + 1) - (x - 1) (x + 1)

= x^{3} - x^{2} + x + x^{2} - x + 1 - (x^{2} - 1)

= x^{3} + 1 - x^{2} + 1

= x^{3} - x^{2} + 2

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Question Text	Find the value of determinant. (i) $∣ ∣ cos θ sin θ - sin θ cos θ ∣ ∣$ (ii) $∣ ∣ x^{2} - x + 1 x + 1 x - 1 x + 1 ∣ ∣$
Answer Type	Text solution:1
Upvotes	150