MATH 1104- Final Exam Guide - Comprehensive Notes for the exam ( 114 pages long!)

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

Document Summary

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? x. 2 + y = 7 x 5y = 10. Remark: geometrically, solution of two linear equations in two variables is the intersection of two lines.