Ex 4.1, 5 - Evaluate determinant - Chapter 4 Class 12 - Ex 4.1

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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise
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Ex 4.1, 5 Evaluate the determinant (i) 3﷮−1﷮−2﷮0﷮0﷮−1﷮3﷮−5﷮0﷯﷯ 3﷮−1﷮−2﷮0﷮0﷮−1﷮3﷮−5﷮0﷯﷯ = 3 0﷮−1﷮−5﷮0﷯﷯ –(–1) 0﷮−1﷮3﷮0﷯﷯ +(–2) 0﷮0﷮3﷮−5﷯﷯ = 3 (0(0) – (– 5) (–1) ) + 1 (0(0) – 3(– 1)) – 2 (0(– 5) – 3(0)) = 3(0 – 5) + 1 (0 + 3) – 2 (0 – 0) = 3(– 5) + 1 (3) + 0 = – 15 + 3 = – 12 Ex 4.1, 5 Evaluate the determinant (ii) 3﷮−4﷮5﷮1﷮1﷮−2﷮2﷮3﷮1﷯﷯ ∆ = 3﷮−4﷮5﷮1﷮1﷮−2﷮2﷮3﷮1﷯﷯ = 3 1﷮−2﷮3﷮1﷯﷯ – (– 4) 1﷮−2﷮2﷮1﷯﷯ + 5 1﷮1﷮2﷮3﷯﷯ = 3(1(1) – 3(-2)) + 4 (1(1) – (2)(-2)) + 5 (1 (3) – 2 (1)) = 3 (1 + 6) + 4 (1 + 4) + 5 (3 – 2) = − 3(7) + 4 (5) + 5(1) = 21 + 20 + 5 = 46 Ex 4.1,5 Evaluate the determinants (iii) 0﷮1﷮2﷮−1﷮0﷮−3﷮−2﷮3﷮0﷯﷯ 0﷮1﷮2﷮−1﷮0﷮−3﷮−2﷮3﷮0﷯﷯ = 0 0﷮−3﷮3﷮0﷯﷯ - 1 −1﷮−3﷮−2﷮0﷯﷯ + 2 −1﷮0﷮−2﷮3﷯﷯ = 0 0 0﷯−3 −3﷯﷯−1 −1 0﷯− −2﷯ −3﷯﷯ 2 −1 3﷯− −2﷯0﷯ = 0 (0 + 9) – 1 (0 – 6) +2 (– 3 – 0) = 0 – 1 (0 – 6) + 2 (− 3 − 0) = – 1(– 6) + 2 (-3) = 6 – 6 = 0 Ex 4.1,5 Evaluate the determinant (iv) 2﷮−1﷮−2﷮0﷮2﷮−1﷮3﷮−5﷮0﷯﷯ ∆ = 2﷮−1﷮−2﷮0﷮2﷮−1﷮3﷮−5﷮0﷯﷯ = 2 2﷮−1﷮−5﷮0﷯﷯ – (– 1) 0﷮−1﷮3﷮0﷯﷯ + (– 2) 0﷮2﷮3﷮−5﷯﷯ = 2(2(0) – (−5)(−1)) +1 (0(0) – 3 (−1)) – 2 (0(-5) – 3 (2)) = 2(0 – 5) + 1 (0 + 3) – 2 (0 – 6) = 2 (– 5) + 1(3) – 2(– 6) = – 10 + 3 + 12 = 2 + 3 = 5

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