MATH125 Lecture Notes - Lecture 11: Solution Set, Elementary Matrix

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Nikita

Document Summary

The following matrices are in row echelon form: Write out the system of linear equations corresponding to the last matrix and solve it. We remind that the last column in an augmented matrix is the vector of constant terms. So the last matrix corresponds to the following system: { x1 + x2 + 2x3 = 1 x3 = 3 x1 = 1 2 3 x2 = 5 x2. There are in nitely many solutions since we may assign x2 any value, say x2 = t, to get the parametric solution. In one word, the basic strategy for solving a linear system is to replace one system with an equivalent system (i. e. one with the same solution set) that is easier to solve. Roughly speaking, use the x1 term in the rst equation of a system to eliminate the x1 terms in the other equations.