Ex 4.4, 1 - Class 12

Transcript

Ex 4.4, 1 Write Minors and Cofactors of the elements of following determinants: (i) 2﷮−4﷮0﷮3﷯﷯ Minor of a11 = M11 = 2﷮−4﷮0﷮3﷯﷯ = 3 Minor of a12 = M12 = 2﷮−4﷮0﷮3﷯﷯ = 0 Minor of a21 = M21 = 2﷮−4﷮0﷮3﷯﷯ = – 4 Minor of a22 = M22 = 2﷮−4﷮0﷮3﷯﷯ = 2 Cofactor of a11 = A11 = ( – 1)1+1 M11 = ( – 1)2 × 3 = 3 Cofactor of a12 = A12 = ( – 1)1+1 M12 = ( – 1)2 × 0 = 0 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) = 2 Ex 4.4, 1 Write Minors and Cofactors of the elements of following determinants: (ii) a﷮c﷮b﷮d﷯﷯ Minor of a11 = M11 = a﷮c﷮b﷮d﷯﷯ = d Min or a12 = M12 = a﷮c﷮b﷮d﷯﷯ = b Minor of a21 = M21 = a﷮c﷮b﷮d﷯﷯ = c Minor of a22 = M22 = a﷮c﷮b﷮d﷯﷯ = a Cofactor of a11 = A11 = ( – 1)1+1 M11 = ( – 1)2 . d = 1 (d) = d Cofactor of a12 = A12 = ( – 1)1+2 M12 = ( – 1)3 . b = – (b) = – b Cofactor of a21 = A21 = ( – 1)2+1 M21 = ( – 1)3 . c = – c Cofactor of a22 = A22 = ( – 1)2+2 M22 = ( – 1)4 (a) = a