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Using Cofactors of Elements of Third Column, Evaluate Triangle = |(1,X,Yz),(1,Y,Zx),(1,Z,Xy)| - Mathematics

Using Cofactors of elements of third column, evaluate `triangle = |(1,x,yz),(1,y,zx),(1,z,xy)|`

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Solution

The given determinant is  `|(1,x,yz),(1,y,zx),(1,z,xy)|`

We have:

∴A13 = cofactor of a13 = (−1)1+3 M13 = (z − y)

A23 = cofactor of a23 = (−1)2+3 M23 = − (z − x) = (x − z)

A33 = cofactor of a33 = (−1)3+3 M33 = (y − x)

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

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APPEARS IN

NCERT Class 12 Maths
Chapter 4 Determinants
Q 4 | Page 126
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