Q. 25.0( 1 Vote )

If A [aij</s

Answer :

Let A be the 2×2 matrix

And |A| = -15

a11a22 – a12a21 = -15 …(i)

Let Mij represent minor of aij and Cij is cofactor of aij.

Mij is the determinant of matrix leaving the ith row and jth column

The cofactor is given by

Cij = (-1) i+jMij

We have to find a21C21 + a22C22

C21 = (-1)2+1M21 = -a12 …since M21 = a12

C22 = (-1)2+2M22 = a11 …since M22 = a11

a21C21 + a22C22 = a21(-a12) + a22a11

a21C21 + a22C22 = a22a11 – a21a12

Using (i)

a21C21 + a22C22 = -15

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