MATH136 Lecture 9: Lecture 9.pdf

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: Robert Sproule

Document Summary

Friday, january 24 lecture 9 : solutions of rref systems of linear equations. Concepts: basic unknowns, free unknowns of a system of linear equations in rref, rank of a coefficient matrix, solutions to a system of linear equation in vector form. 9. 1 we now consider ways of representing a family of solutions for an rref system of linear equations. 9. 2 theorem if a system of linear equations has more than one solution then it has infinitely many solutions. The ith equation can be written as (ai1, , ain) (x1, , xn) = ai x = bi. Suppose u = (u1, , un) and v = (v1, , vn) are distinct solutions to this system. Then for i = 1 to m and any scalar we have. Since u and v are distinct if then u + (u v) u + (u v).