      1. Chapter 4 Class 12 Determinants
2. Serial order wise
3. Ex 4.4

Transcript

Ex 4.4, 2 Write Minors and Cofactors of the elements of following determinants: (i) 1 0 0 0 1 0 0 0 1 Minor of a11 = M11 = 1 0 0 0 1 0 0 0 1 = 1 0 0 1 = 1(1) 0 = 1 Minor of a12 = M12 = 1 0 0 0 1 0 0 0 1 = 0 0 0 1 = 0 0 = 0 Minor of a13 = M13 = 1 0 0 0 1 0 0 0 1 = 0 1 0 0 = 0 0 = 0 Minor of a21 = M21 = 1 0 0 0 1 0 0 0 1 = 0 0 0 1 = 0 0 = 0 Minor of a22 = M22 = 1 0 0 0 1 0 0 0 1 = 1 0 0 1 = 1 0 = 1 Minor of a23 = M23 = 1 0 0 0 1 0 0 0 1 = 1 0 0 0 = 0 0 = 0 Minor of a31 = M31 = 1 0 0 0 1 0 0 0 1 = 0 0 1 0 = 0 0 = 0 Minor of a32 = M32 = 1 0 0 0 1 0 0 0 1 = 1 0 0 0 = 0 0 = 0 Minor of a33 = M33 = 1 0 0 0 1 0 0 0 1 = 1 0 0 1 = 1 0 = 1 Cofactor of a11 = A11 = ( 1)1+1 M11= ( 1)2 1= 1 1 = 1 Cofactor of a12 = A12 = ( 1)1+2 M12= ( 1)3 0 = 0 Cofactor of a13 = A13 = ( 1)1+3 M13 = ( 1)4 0 = 0 Cofactor of a21 = A21 = ( 1)2+1 M21 = ( 1)3 0 = 0 Cofactor of a22 = A22 = ( 1)2+2 M22 = ( 1)4 1 = 1 . 1 = 1 Cofactor of a23 = A23 = ( 1)3 + 1 M23 = ( 1)4 0 = 0 Cofactor of a31 = A31 = ( 1)3 + 1 M31 = ( 1)4 0 = 0 Cofactor of a32 = A32 = ( 1)3 + 2 M32 = ( 1)5 0 = 0 Cofactor of a33 = A33 = ( 1)3 + 3 M33 = ( 1)6 . 1 = 1 . 1 = 1 Ex 4.4, 2 Write Minors and Cofactors of the elements of following determinants: (ii) 1 0 4 3 5 1 0 1 2 Minor of a11 = M11= 1 0 4 3 5 1 0 1 2 = 5 1 1 2 = 5(2) 1( 1)= 10 + 1= 11 Minor of a12 = M12 = 1 0 4 3 5 1 0 1 2 = 3 1 0 2 = 6 0 = 6 Minor of a13 = M13 = 1 0 4 3 5 1 0 1 2 = 3 5 0 1 = 3 0 = 3 Minor of a21 = M21 = 1 0 4 3 5 1 0 1 2 = 0 4 1 2 = 0 4 = 4 Minor of a22 = M22 = 1 0 4 3 5 1 0 1 2 = 1 4 0 2 = 2 0 = 2 Minor of a23 = M23 = 1 0 4 3 5 1 0 1 2 = 1 0 0 1 = 1 0 = 1 Minor of a31 = M31 = 1 0 4 3 5 1 0 1 2 = 0 4 5 1 = 0 20 = 20 Minor of a32 = M32 = 1 0 4 3 5 1 0 1 2 = 1 4 3 1 = 1 12 = 13 Minor of a33 = M33 = 1 0 4 3 5 1 0 1 2 = 1 0 3 5 = 5 0 = 5 Cofactor of a11 = A11 = ( 1)1+1 M11 = ( 1)2 11= 1 11 = 11 Cofactor of a12 = A12 = ( 1)1+2 M12 = ( 1)3 . 6 = ( 1)6 = 6 Cofactor of a13 = A13 = ( 1)1+3 M13 = ( 1)4 . 3 = (1) 3 = 3 Cofactor of a21 = A21 = ( 1)2+1 M21 = ( 1)3 . ( 4) = ( 1) ( 4) = 4 Cofactor of a22 = A22 = ( 1)2+2 M22 = ( 1)4 . (2) = (1) . (2) = 2 Cofactor of a23 = A23 = ( 1)2 + 3 M23 = ( 1)5 (1) = ( 1) (1) = 1 Cofactor of a31= A31 = ( 1)3 + 1 M31 = ( 1)4 ( 20) = 1 . ( 20) = 20 Cofactor of a32= A32= ( 1)3 + 2 M32 = ( 1)5 . ( 13) = ( 1) ( 13) = 13 Cofactor of a33 = A33 = ( 1)3 + 3 M33 = ( 1)6 . (5) = ( 1) . (5) = 5

Ex 4.4 