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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