In a calculus course, you'll see more complicated functions, and use calculus to analyze them. We're not going to look at anything more complicated than linear functions. But we are going to look at more than one at once, so things get complicated in a different way. Vector Equation Matrix Equation Transformation Looking at something from a different point of view may give a new insight and enable us to solve the problem more easily. How a solution can be represented by a point on a graph.
Equations are lines.
Lines can meet in different ways. Transformations How to think about a linear system as a transformation, and lots of other interesting transformations. Vector spaces Some interesting properties of solutions of linear systems. We'll see problems with many solutions. We'll also study dimension.