Loading...
In this section, several theorems about determinants are derived p(a1) = 0, so we have p(x)=(x?a1)p1(x) by the factor theorem (see Appendix D)
(ii) Co-factor of an element aij is given by Aij = (–1)i+j Mij (iii) Value of determinant of a matrix A is obtained by the sum of products of elements of a row
Why are combinatorialists so fascinated by determinant evaluations? A simplistic answer to this question goes as follows Clearly, binomial coefficients ( n k )
Theorem 1 (Main properties of n × n determinants) Let because the factor in the numerator in the right hand side is precisely det(A) = ? Slide 10
reasoning that shows that the product of determinant factors comes out the same no matter This theorem is imporant for all sorts of reasons
which contains such factors It is now proposed to examine a direct method for finding the algebraic composition of the determinant M of the coeffi-