MA122 Study Guide - Midterm Guide: Elementary Matrix, Row Echelon Form, Augmented Matrix
Document Summary
Print version of the lectures in ma122 introductory linear algebra presented in september. 13, 2018 by c(cid:13)adam metzler from the department of mathematics at wilfrid laurier university. Solving systems of equations - brute force: suppose we wanted to solve the following system: x1 + x2 + x3 = 7 , 4x1 + 2x2 x3 = 4 , 5x1 + x2 + 2x3 = 5 : we could use (1) to write x1 in terms of x2 and x3: x1 = 7 x2 x3 , we could then plug this into (2) to write. 4(7 x2 x3) + 2x2 x3 = 4 , which can be rearranged to get x2 = x3 . Brute force, cont"d: now plug (5) into (4) to get x1 = De nition and notation: associated with any linear system is an augmented matrix a1,1x1 + a1,2x2 + . + a1,nxn = b1 , a2,1x1 + a2,2x2 + .
