Determinant

Determinant-1:

Definition-3:

Let A = [ a_ij ] be n n matrix. Then the expansion of det (A) along the ith row is defined by;

det (A) = |A| =

and the expansion of det (A) along the jth column is defined by;

Example-2:

Example-3:

Adjoint Matrix:

Let A = [ a_ij ] be n n matrix. The n n matrix adj is called the Adjoint of A is the matrix whose (i,j) the entry is the cofactor A_ij or a_ij. Thus

Exampel-1:

We first compute the cofactor of A. we have