Fundamentals of Matrix Algebra, 2011a

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You have probably encountered systems of linear equaons before; you can probably
remember solving systems of equaons where you had three equaons, three
unknowns, and you tried to find the value of the unknowns. In this chapter we will
uncover some of the fundamental principles guiding the soluon to such problems.
Solving such systems was a bit me consuming, but not terribly difficult. So why
bother? We bother because linear equaons have many, many, many applicaons,
from business to engineering to computer graphics to understanding more mathematics.
And not only are there many applicaons of systems of linear equaons, on most
occasions where these systems arise we are using far more than three variables. (Engineering
applicaons, for instance, oen require thousands of variables.) So geng
a good understanding of how to solve these systems effecvely is important.
But don’t worry; we’ll start at the beginning.
1.1 Introducon to Linear Equaons
AS YOU READ ...
. . .
1. What is one of the annoying habits of mathemacians?
2. What is the difference between constants and coefficients?
3. Can a coefficient in a linear equaon be 0?
We’ll begin this secon by examining a problem you probably already know how
to solve.
. Example 1 .Suppose a jar contains red, blue and green marbles. You are told
that there are a total of 30 marbles in the jar; there are twice as many red marbles as