Answer :

To evaluate a determinant using cofactors, Let

B =

Expanding along Row 1

B =

B = a_{11} A_{11} + a_{12} A_{12} + a_{13} A_{13}

[Where A_{ij} represents cofactors of a_{ij} of determinant B.]

B = Sum of product of elements of R_{1} 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

A_{21} = (-1)^{2+1} × M_{21} = (-1) × = (-1) × (3 × 3 – 8 × 2) = (-1) × (-7) = 7

A_{22} = (-1)^{2+2} × M_{22} = 1 × = (5 × 3 – 8 × 1) = 7

A_{23} = (-1)^{2+3} × M_{23} = (-1) × = (-1) × (5 × 2 – 3 × 1) = (-1) × 7 = -7

[Where A_{ij} = (-1)^{i+j} × M_{ij}, M_{ij} = Minor of i^{th} row & j^{th} column]

Therefore,

Δ = a_{21}A_{21} + a_{22}A_{22} + a_{23}A_{23}

Δ = 2 × 7 + 1 × (-7) = 14 - 7 = 7

Ans: Δ = 7

Rate this question :

If <span lang="ENMathematics - Board Papers

Find the minor ofMathematics - Board Papers

If <span lang="ENMathematics - Board Papers

Fill in theMathematics - Exemplar

If <span lang="ENMathematics - Board Papers