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Question -

Using Cofactors of elements of third column,evaluate



Answer -

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 tothe sum of the product of the elements of the second row with theircorresponding cofactors.

Hence,  

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