MAT 1302 Lecture Notes - Lecture 4: Row Echelon Form, Solution Set, Linear Combination

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1302
• Professor: Aaron Tikuisis

Document Summary

Mat1302 - lecture 4 - rref possibilities and vector equations. When put into the reduced row echelon form, a system of linear equations has 3 possible outcomes. 1- the system is inconsistent: detectable with the equation 0=1. 2- the system has one solution: if there are no free variables or every variable column is a pivot column. 3- the system has multiple solutions: identify the free variables, write the dependant variables in terms of the free variables and then do the solution set. Vector operations: a vector of m size is written as a vertical list of numbers. A linear combination of vectors where are scalars. Example: linear combination of weight (5,-3,6) is the weight on u in a linear combination. Vector equations: if the scalar equation in a linear combination is treated as variables, you can create a vector equation. Important: vector equations, system of linear equations and augmented matrix are equivalent to each other.