Using Cofactors of elements of second row- evaluate - 5 3 8- 2 0 1- 1 2 3 -

The given determinant is. We have: M21 = ∴A21 = cofactor of a21 = (−1)2+1 M21 = 7 M22 = ∴A22 = cofactor of a22 = (−1)2+2 M22 = 7 M23 = ∴A23 = cofactor of ...

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Standard XII

Mathematics

Evaluation of a Determinant

Using Cofacto...

Question

Using Cofactors of elements of second row, evaluate.

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Solution

The given determinant is.

We have:

M₂₁=

∴A₂₁= cofactor of a₂₁= (−1)²⁺¹ M₂₁ = 7

M₂₂=

∴A₂₂= cofactor of a₂₂= (−1)²⁺² M₂₂ = 7

M₂₃=

∴A₂₃= cofactor of a₂₃= (−1)²⁺³ M₂₃ = −7

We know that Δ is equal to the sum of the product of the elements of the second row with their corresponding cofactors.

∴Δ = a₂₁A₂₁ + a₂₂A₂₂ + a₂₃A₂₃ = 2(7) + 0(7) + 1(−7) = 14 − 7 = 7

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