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Ex 4.1, 2 - Evaluate determinant (i) |cos sin -sin cos| - Finding determinant of a 2x2 matrix

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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise
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Ex 4.1, 2 Evaluate the determinant (i) cos θ﷮−sin θ﷮sin θ﷮cos θ﷯﷯ cos θ﷮−sin θ﷮sin θ﷮cos θ﷯﷯ = cos θ(cos θ) − (sin θ) (- sin θ) = cos2 θ + sin2 θ = 1 Ex 4.1,2 Evaluate the determinant (ii) x2−x+1﷮x−1﷮x+1﷮x+1﷯﷯ x2−x+1﷮x−1﷮x+1﷮x+1﷯﷯ = (x2 − x + 1) (x + 1) − (x − 1)(x + 1) = (x2 − x + 1) (x + 1) − (x2 − 12) = [(x2 − x + 1) x + (x2 − x + 1)1] − (x2 − 1) = (x3 − x2 + x + x2 − x + 1) − (x2 − 1) = x3 + 0 + 0 + 1 − x2 + 1 = x3 – x2 + 1 + 1 = x3 − x2 + 2

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