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Introduction
One of the fundamental lessons of calculus is that many complicated problems can be solved by taking linear approximations to complicated functions. This often produces several linear equations for which we want to know when they are simultaneously true; that is, we would like to solve this
system of linear equations. This chapter centers around that fundamental question, building off of your intuition for what happens in the simplest case of two equations in two variables. Geometrically, this corresponds to finding the intersection of two lines in the plane. As we introduce more variables, we quickly lose our ability to visualize this process geometrically, so we will introduce a tool called a
matrix to help us solve these.
Motivating Question. How can we solve systems of linear equations?
