MATH 204 Lecture Notes - Lecture 1: Augmented Matrix, Solution Set, Linear Algebra
Document Summary
The central problem of linear algebra is the solutions of linear equations. Remark: a linear equation does not involve any produces or roots of variables. Next, what is a solution of a linear equation? a1x1+a2x2+ +anxn = b. One solution of such equation is a sequence of n numbers s1, s2 sn such that the equation is satisfied when x1=s1, x2=s2 xn=sn. The set of all solutions of this equation is called its solution set or the general solution of the equation. Solution set: x=t, y=2t-1/2 ; (here t is a parameter. ) If we assign x an arbitrary value t, we obtain (x=t, y=2t-1/2) , which describe the solution set of the equation, in terms of an arbitrary number t, which is called parameter. A system of linear equations or a linear system is a finite set of linear equations in variables. a11x1+a12x2+ +a1nxn = b1 a21x1+a22x2+ +a2nxn = b2 an1x1+an2x2+ +annxn= bn.
