MAT 1302 Chapter Notes - Chapter 1-6: Elementary Matrix, Augmented Matrix, Free Variables And Bound Variables

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1302
• Professor: Hadi Salmasian

Document Summary

The solution to a linear equation is the point of intersection of two lines, i. e. (1, -1). A linear equation that does not have a solution is called inconsistent. If the rightmost column of the augmented matrix is a pivot column, then the system is inconsistent. Two equations that are multiples of each other result in infinitely many solutions, they are essentially the same equation. A system of linear equations is a collection of linear equations in the same set of variables. The solution set of a linear equation is the set of all lists of numbers (x) such that the values solve the system. Two matrices are called row equivalent if one can get from one to the other by a sequence of elementary row operations. A basic variable is one corresponding to a pivot column (a column containing a pivot position). If all the variables are basic, then the system has a unique solution.