MATH125 Lecture Notes - Lecture 3: Solution Set

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Vladimir Chernousov

Document Summary

The common notation for a linear equation in r^2 is: ax+by=c where x and y are variables, and a, b, and c are coefficients. If the variables are added, it is a linear equation. Instead we would pick one variable and one coefficient. Definition: in a linear equation in r^n number of variables, x1+x2++xn is the equation which can be written as a1x1+a2x2++anxn=b. Where x1,x2,,xn are variables, a1,a2,,an are the coefficients and b is the constant term. Definition: if b=0 then the linear equation is of the form a1x1+a2x2++anxn=0 and is called homogenous. Definition: assume we are given a linear equation, let a1x1+a2x2++anxn=b. 15-15=-1, so s is a solution for the linear equation. Remark: consider 3x-4y=-1, any point on the line is a solution. January 20, 2016 ax1x1+a2x2++anxn=b where x1xn are variables a1an are coefficients and is the constant term. It is important to notes that s may not be unique, there may be multiple solutions to the linear equations.