Math 261 Section 1.1 Systems of Linear Equations
Definition: Alinear equation in the variables x1, ..., xnis an equation that can be written in
the form
a1x1+a2x2+···+anxn=b
Definition: Asystem of linear equations is a collection of one or more linear equations
involving the same variables. In other words, it’s just a list of linear equations.
Definition: Asolution to a system of linear equations is a list of numbers, usually notated
(s1,s
2,...,s
n)ors1,s
2,...,s
nand usually referred to as a point or vector depending on the
context, which satisfies all of the equations in the system.
1. Given the system of linear equations
x1−2x2+x3=0
2x2−8x3=8
5x1−5x3=10
Determine the coefficient matrix and the augmented matrix and then solve the system
using the elimination method, showing the system of equation manipulation and matrix
manipulation side by side. What do each of these equations represent and what does the
solution to the system represent geometrically?
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