MATH136 Lecture Notes - Identity Matrix, General Idea, Elementary Matrix

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: Robert Sproule

Document Summary

Friday, march 14 lecture 27 : elementary matrices and invertibility. 27. 0 recall an ero can always be reversed by an ero. The ero pij can be undone by applying pij again. The ero crj can be undone by applying (1/c)rj . The ero cri + rj can be undone by applying cri + rj. Two matrices a and b are row-equivalent if there is a finite sequence of elementary row operations which, when applied successively, transform the matrix a into the matrix b. We will use the notation to say a is row-equivalent to b . 27. 1. 1 example the following chain of ero"s applied to a shows that a is row- equivalent to b. 27. 1. 2 observation the matrix a is row-equivalent to b if and only if arref = brref. Proof : ( ) if a ~ b, A ero"s b ero"s brref a ero"s brref = arref ( ) if brref = arref,