MATH125 Lecture Notes - Lecture 5: Row Echelon Form, Elementary Matrix, Free Variables And Bound Variables

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Vladimir Chernousov

Document Summary

January 29, 2016 if there are multiple solutions to a linear system, the solution set will be denoted in vector from, as a set of parameters example. [s ] this can then be broken down into parameters and terms: This is the general solution in vector form. It is the set of all linear combinations of u and v. It contains the origin, and if t=1,s=0 it is u, and if t=0,s=1 it is v. The solution set is the vectors t[1,1,0,0] and s[-1,0,1,1] that pass through the point (2,0,1,0) Definition: variables corresponding to the leading entries are called leading variables. Our strategy is to express leading variables in terms of free variables. Definition: the entry of a matrix chosen to be the leading entry is called the pivot entry, elements in pivot position are called pivot elements. The columns containing pivot elements are called pivot columns.