We have already discussed systems of linear equations and how this is related to matrices. In this chapter we will learn how to write a system of linear equations succinctly as a matrix equation, which looks like where is an matrix, is a vector in and is a variable vector in As we will see, this is a powerful perspective. We will study two related questions:
- What is the set of solutions to
- What is the set of so that is consistent?
The first question is the kind you are used to from your first algebra class: what is the set of solutions to The second is also something you could have studied in your previous algebra classes: for which does have a solution? This question is more subtle at first glance, but you can solve it in the same way as the first question, with the quadratic formula.