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Question 4:
Using Cofactors of elements of third column, evaluate
The given determinant is
.
We have:
M13 = 
M23 = 
M33 = 
∴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.
Hence, 
