MATH-M 303 Lecture Notes - Lecture 1: Tuple, Coefficient Matrix, Linear Equation
Document Summary
M303 lecture 1 notes- solving systems of linear equations. Linear equation in variables (cid:2869), ,(cid:3041)- equation of form (cid:1853)(cid:2869)(cid:2869)+(cid:1853)(cid:2870)(cid:2870)+(cid:1710)+(cid:1853)(cid:3041)(cid:3041)=(cid:1854), where coefficients (cid:1853)(cid:3036) and (cid:1854) are real numbers. Linear system- collection of 1 or more linear equations in the same variables (cid:2869), ,(cid:3041: ex. (cid:885)(cid:2869) (cid:884)(cid:2870)=(cid:888) (cid:891)(cid:2870)=(cid:883)(cid:882, ex. (cid:2869) (cid:2870)+(cid:2871)=(cid:884) (cid:2869)+(cid:2871)=(cid:882) Solution of system in (cid:2869), ,(cid:3041)- ordered (cid:1866)-tuple (cid:4666)(cid:2869), ,(cid:3041)(cid:4667) of real numbers (cid:3036), which, when substituted for (cid:3036), result in all equations being true: ex. Can check by inspection that (cid:4666)(cid:883), (cid:884), (cid:883)(cid:4667) is solution to second equation above. Two systems equivalent when they have same solution set: solution set- set of all possible solutions to linear system. All points (parallel identical lines, infinitely many solutions) Augmented matrix- to keep track of right sides: system is consistent if it has solutions; inconsistent otherwise, ex. There are 2 matrices associated with a linear system given the system:
