#### Question

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:

∴A_{13 }= cofactor of *a*_{13 }= (−1)^{1+3} M_{13} = (*z − y*)

A_{23 }= cofactor of *a*_{23 }= (−1)^{2+3} M_{23} = − (*z − x*) = (*x − z*)

A_{33 }= cofactor of *a*_{33 }= (−1)^{3+3} M_{33} = (*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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#### Reference Material

Solution for question: Using Cofactors of Elements of Third Column, Evaluate Triangle = |(1,X,Yz),(1,Y,Zx),(1,Z,Xy)| concept: Minors and Co-factors. For the courses CBSE (Arts), CBSE (Commerce), CBSE (Science)