MTH 210 Study Guide - Midterm Guide: Royal Institute Of Technology, Free Variables And Bound Variables, 1

• School: University of Miami
• Department: Mathematics
• Course: MTH 210
• Professor: Galloway

Document Summary

1. 1: intro to systems of linear equations: define linear equation, give general form. A linear equation with n variables (cid:1876)(cid:2869),(cid:1876)(cid:2870), ,(cid:1876)(cid:3041) can be expressed in the general form (cid:1853)(cid:2869)(cid:1876)(cid:2869)+ (cid:1853)(cid:2870)(cid:1876)(cid:2870)+(cid:1710)+(cid:1853)(cid:3041)(cid:1876)(cid:3041)=(cid:1854) where (cid:1853)(cid:2869),(cid:1853)(cid:2870), ,(cid:1853)(cid:3041) are constants and not all nonzero: define homogeneous linear equation. A linear equation in which b=0 is a homogeneous linear equation: define system of linear equations. A system of linear equations involves more than one (but a finite number of) linear equations: define unknowns. The unknowns are the variables in the equation(s) you are solving for: define solution set, give notation. The solution set is the set of all solutions to a linear system. {(cid:4666)(cid:1871)(cid:2869),(cid:1871)(cid:2870), ,(cid:1871)(cid:2871)(cid:4667)|(cid:1868) } where p is the free variable under the condition it is any real number and (cid:1876)(cid:2869)=(cid:1871)(cid:2869),(cid:1876)(cid:2870)=(cid:1871)(cid:2870), ,(cid:1876)(cid:3041)=(cid:1871)(cid:3041) make each equation a true statement. The empty set is written as either { } or : explain the 3 possibilities for linear systems.