If and Ai, Bi, Ci are cofactors of ai, bi, ci then a1B1 + a2B2 + a3B3 =

Engineering

Mathematics

Introduction to Determinants

Question

If $A = [\begin{array}{ccc} a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3} \end{array}]$ and A_i, B_i, C_i are cofactors of a_i, b_i, c_i then a₁B₁ + a₂B₂ + a₃B₃ =

|A|

|A|²

2|A|

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Sum of product of any row with its corresponding cofactors io Determinant

a₁A₁ + b₁B₁ + c₁C₁ = a₂A₂ + b₂B₂ + c₂C₂ = a₃A₃ + b₃B₃ + c₃C₃ = Δ

Sum of product of any row with another row's wfactor is zero

∴ a₁B₁ + a₂B₂ + a₃B₃ = 0 option (A)

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