MA 35100 Lecture Notes - Lecture 7: Augmented Matrix, European Food Safety Authority, Solution Set
Document Summary
" elementary row operations ( eros) : allowed moves. Add a multiple of one row to another row. Scale a row by a non - zero scalar. " if a sequence of eros transforms a matrix a into a matrix b , we say that a and b are row equivalent . inverse. , b efsa as every ero can be undone by an ero . If a and b are row equivalent and are augmented matrices for systems of les , then their systems have the same solution set . An eschelon (respectively reduced form of a matrix a is a matrix b that is row equivalent to a and it is in eschelon (respectively reduced) form . Theorems 1. 4 , 1. 6: every matrix is row equivalent to a matrix in eschelon form (actually many) (1. 4) and to exactly one in reduced form (i. Gaussian elimination : turn a matrix into its rref using eros.
