This preview shows page 1. Sign up to view the full content.
Unformatted text preview: R is a eld. One can reduce a given matrix A to triangular form by elementary row operations: interchanging two rows or adding a multiple of one row to another row. Operations of the rst type change the sign of the determinant while operations of the second type leave the determinant unchanged. If B is an upper triangular matrix obtained from A in this manner, then det .A/ D . 1/ k det .B/ , where k is the number of row interchanges performed in the reduction. But det .B/ is the product of the diagonal entries of B , by part (c) of Corollary 8.3.9 . The same method works for matrices over an integral domain, as one can work in the eld of fractions; of course, the determinant in the eld of fractions is the same as the determinant in the integral domain....
View
Full
Document
This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra, Determinant

Click to edit the document details