Ex 4.4, 3 - Using Cofactors of elements of second row, evaluate - Finding Minors and cofactors

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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise
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Ex 4.4, 3 Using Cofactors of elements of second row, evaluate ∆ = 5﷮3﷮8﷮2﷮0﷮1﷮1﷮2﷮3﷯﷯ Δ = a21 A21 + a22 A22 + a23 A23 a21 = 2, a21 = 0, a21 = 1, Calculating cofactor of second row i.e. A21 , A22 , And A23 M21 = 5﷮3﷮8﷮2﷮0﷮1﷮1﷮2﷮3﷯﷯= 3﷮8﷮2﷮3﷯﷯ = 3 × 3 – 2 × 8 = 9 – 16 = – 7 M22 = 5﷮3﷮8﷮2﷮0﷮1﷮1﷮2﷮3﷯﷯ = 5﷮8﷮1﷮3﷯﷯ = 5 × 3 – 8 × 1= 15 – 8 = 7 M23 = 5﷮3﷮8﷮2﷮0﷮1﷮1﷮2﷮3﷯﷯ = 5﷮3﷮1﷮2﷯﷯ = 5 × 2 – 1 × 3 = 10 – 3 = 7 Cofactor of a21 = A21 = (– 1)2+1 M21 = (– 1)3 × – 7 = – 1 × – 7 = 7 Cofactor of a22 = A22 = ( – 1)2+2 M22 = ( – 1)4 . 7 = 7 Cofactor of a23 = A23 = (−1)2 + 3 M31 = (–1)5 . (7) = (– 1) (7) = – 7 Now Δ = a21 A21 + a22 A22 + a23 A23 = 2 × 7 + 0 × 7 + 1 × (−7) = 14 + 0 + 7 = 7

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