MATH 1104 Lecture Notes - Lecture 1: Row Echelon Form, Alaca, Linear Map

• School: Carleton University
• Department: Mathematics
• Course: MATH 1104
• Professor: Ayse Alaca

Document Summary

Lecture notes c(cid:13)prepared by ay se and s aban alaca. These notes replace neither the textbook nor the lectures. A system of linear equations (or a linear system) is a collection of one or more linear equations involving the same set of variables, say x1, x2, , xn. 2x1 + 2x2 + 5x3 = 3. is a linear system and (x1, x2, x3) = (1, 0, 1) is a solution for this system. (x1, x2, x3) = (2, 4, 3) is also a solution for this system. The set of all possible solutions is called the solution set of the linear system. Two linear systems are called equivalent if they have the same solution set. Example: x + y = 4 x y = 2. 13x + 3y = 42 are equivalent systems since the solution set for both of them is {(3, 1)}. Which of the following system(s) is/are linear? x2 + y = 7 x 5y = 10.