Cofactor and the adjoint formulafor matrix inverseCofactors are defined in a similar way as in the 3x3 case.- The cofactor of the (ij)-entry of a matrix A, denoted by Ci, isdefined as (-1)i+j Ai, where A is the determinant of the sub-matrix obtained byremoving thei-throwandthej-thcolumn.We have similar expansion along a row or a column (alsocalled the Laplace expansion) as in the 3x3 case.The adjoint formula:transposenxn identityALadjoint of AT0C110Cin10C12a11a12ain000C21C2n1a22a22a2na22=detA......::.....:..1Cn1000Cnnanlan2annan2The formula in this form holds when det A = O alsokshumENGG2013
Cofactor and the adjoint formula for matrix inverse • Cofactors are defined in a similar way as in the 3x3 case. – The cofactor of the (i,j)-entry of a matrix A, denoted by Cij, is defined as (–1)i+j Aij, where A is the determinant of the submatrix obtained by removing the i-th row and the j-th column. • We have similar expansion along a row or a column (also called the Laplace expansion) as in the 3x3 case. • The adjoint formula: kshum ENGG2013 A nxn identity adjoint of A The formula in this form holds when det A = 0 also transpose
CAESARCIPHERkshumENGG2013
CAESAR CIPHER kshum ENGG2013