# MATH 125 Study Guide - Final Guide: Row Echelon Form, Augmented Matrix, Gaussian Elimination

## Document Summary

Note: some of the solutions here are just sketches (the main purpose is to enable you to check your own answers). In particular, row reduction of matrices is omitted completely. In your exam, however, you should show all your work, and give suitable justi cation for your answers. When row reducing a matrix, you should clearly indicate which row operations have been applied at each step of the process. 1: is span , is span , is span . 1: for which values of a, is span . Solution: a) no, 2 vectors cannot be a spanning set of r3: let ~v = a b c. 0 a 2c b c b. Clearly the system is consistent if and only if a 2c b = 0. But there are in nitely many choices of a, b, c for which this equation does not hold: a simple example is a = 1,