Q. 1 A3.9( 51 Votes )

Write Minors and

Answer :

Minor: Minor of an element aij of a determinant is the determinant obtained by removing ith row and jth column in which element aij lies. It is denoted by Mij.

Cofactor: Cofactor of an element aij, Aij = (-1)i+j Mij.


Minor of element aij = Mij


a11 = 2, Minor of element a11 = M11 = 3


Here removing 1st row and 1st column from the determinant we are left out with 3 so M11 = 3.


Similarly, finding other Minors of the determinant


a12 = -4, Minor of element a12 = M12 = 0


a21 = 0, Minor of element a21 = M21 = -4


a22 = 3, Minor of element a22 = M22 = 2


Cofactor of an element aij, Aij = (-1)i+j × Mij


A11 = (-1)1+1 × M11 = 1 × 3 = 3


A12 = (-1)1+2 × M12 = (-1) × 0 = 0


A21 = (-1)2+1 × M11 = (-1) × (-4) = 4


A22 = (-1)2+2 × M22 = 1 × 2 = 2


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