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Ex 4.4, 3 - Using Cofactors of elements of second row, evaluate

Ex 4.4, 3 - Chapter 4 Class 12 Determinants - Part 2

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Ex 4.4, 3 Using Cofactors of elements of second row, evaluate ∆ = |■8(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 = |■8(5&3&8@2&0&1@1&2&3)|= |■8(3&8@2&3)| = 3 × 3 – 2 × 8 = 9 – 16 = –7 M22 = |■8(5&3&8@2&0&1@1&2&3)| = |■8(5&8@1&3)| = 5 × 3 – 8 × 1= 15 – 8 = 7 M23 = |■8(5&3&8@2&0&1@1&2&3)| = |■8(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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.