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Question
Using Cofactors of elements of second row, evaluate Δ = `|(5,3,8),(2,0,1),(1,2, 3)|`.
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Solution
The co-sections of the second row will be like this:
A21 = `(-1)^(2 + 1) |(3,8),(2,3)|`
= (−1) × [3 × 3 − 2 × 8]
= 7
A22 = `(- 1)^(2 + 2) |(5,8),(1,3)|`
= 1 × [5 × 3 − 1 × 8]
= 7
A23 = `(-1)^(2 + 3) |(5,3),(1,2)|`
= (−1) [5 × 2 − 3 × 1]
= −7
∴ Δ = a21 × A21 + a22 × A22 + a23 × A23
= 2 × 7 + 0 × 7 + 1 × (−7)
= 14 + 0 − 7
= 7
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