Q. 33.9( 55 Votes )

# Using Cofactors o

To evaluate a determinant using cofactors, Let

B = Expanding along Row 1

B = B = a11 A11 + a12 A12 + a13 A13

[Where Aij represents cofactors of aij of determinant B.]

B = Sum of product of elements of R1 with their corresponding cofactors

Similarly, the determinant can be solved by expanding along column

So, B = sum of product of elements of any row or column with their corresponding cofactors Cofactors of second row

A21 = (-1)2+1 × M21 = (-1) × = (-1) × (3 × 3 – 8 × 2) = (-1) × (-7) = 7

A22 = (-1)2+2 × M22 = 1 × = (5 × 3 – 8 × 1) = 7

A23 = (-1)2+3 × M23 = (-1) × = (-1) × (5 × 2 – 3 × 1) = (-1) × 7 = -7

[Where Aij = (-1)i+j × Mij, Mij = Minor of ith row & jth column]

Therefore,

Δ = a21A21 + a22A22 + a23A23

Δ = 2 × 7 + 1 × (-7) = 14 - 7 = 7

Ans: Δ = 7

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