If then cofactor of a21 is :

Engineering

Mathematics

Introduction to Matrix

Question

If $A = | \begin{array}{lll} a & b & c \\ b & c & a \\ c & a & b \end{array} |$ then cofactor of a₂₁ is :

b² – ac

bc – a²

a² – bc

ac – b²

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By property of co-factor of matrix(2),
cofactor of a_ij = M_ij × (– 1)^i+j
∴ minor of $a_{21} = ∣ \begin{array}{cc} a_{12} & a_{13} \\ a_{32} & a_{33} \end{array} ∣ = ∣ \begin{array}{cc} b & c \\ a & b \end{array} ∣$
M₂₁ = b² – ac
So, co factor of a₂₁ = M₂₁ × (– 1)¹⁺² = – M₂₁
= ac – b²