MATH 3A Lecture Notes - Lecture 1: Augmented Matrix, Free Variables And Bound Variables, Linear Combination

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 3A
• Professor: Alex Figotin

Document Summary

Midterm 1 concept: consistent: a unique solution or infinitely many solutions, a system of linear equations is collection of one or more linear equations with the. If v belongs to span (u), then span (u, v) = span (u), which is a line. If a is an (m x n) matrix with columns a(cid:1005), a(cid:1006), , a(cid:374), and b is a vector in rm, then the matrix equation ax=b has the same set of solutions as the vector equation x(cid:1005)a(cid:1005) + . The (cid:272)olle(cid:272)tio(cid:374) of all li(cid:374)ea(cid:396) (cid:272)o(cid:373)(cid:271)i(cid:374)atio(cid:374)s of a(cid:1005), , a(cid:374) is pa(cid:374) {a(cid:1005), , a(cid:374)}. So if every b belongs to rm is a li(cid:374)ea(cid:396) (cid:272)o(cid:373)(cid:271)i(cid:374)atio(cid:374) of a(cid:1005), , a(cid:374), the(cid:374) pa(cid:374) {a(cid:1005), , a(cid:374)} = rm: let a (cid:271)e a(cid:374) (cid:894)(cid:373) (cid:454) (cid:374)(cid:895) (cid:373)at(cid:396)i(cid:454). If a homogeneous linear system has a non-trivial solution, then it must have infinitely many solutions.