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Question
Using cofactors of elements of second row, evaluate |A|, where A = `[(5, 3, 8),(2, 0, 1),(1, 2, 3)]`
Solution
A = `[(5, 3, 8),(2, 0, 1),(1, 2, 3)]`
Cofactr of 2, A21 = `(- 1)^(2 + 1) |(3, 8),(2, 3)|`
= – [9 – 16]
= 7
Cofactr of 0, A22 = `(- 1)^(2 + 2) |(5, 8),(1, 3)|`
= 15 – 8
= 7
Cofactr of 1, A23 = `(- 1)^(2 + 3) |(5, 3),(1, 2)|`
= – [10 – 3]
= – 7
∴ |A| = a21 A21 + a22 A22 + a23 A23
= 2 × 7 + 0 × 7 + 1 × – 7
= 14 – 7
|A| = 7
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