MATH 1025 Lecture Notes - Row Echelon Form, Augmented Matrix, Gaussian Elimination
11 Apr 2023
School
Department
Course
Professor
Document Summary
Class 3: ref, rref and solving systems of linear equations. Last time, we saw a simple form of matrices: In addition to ref, there is an even simpler form matrices can be in: 8>< (a) write down the associated augmented matrix for the system of equations. The location of the leading entries of a matrix in ref are called pivots. The following algorithm produces a matrix that is in. Step 1: begin with the leftmost nonzero column. If necessary, interchange rows so that a nonzero entry is at the top (in a pivot position). Step 2: by adding multiples of the rst row to the rows below it, create zeros in all positions below this pivot (in the column containing this pivot). Step 3: now ignore the row and column containing this pivot. Repeat the process until there are no more nonzero rows to modify.
