In the last chapter we learned how to solve systems of equations, and along the way, we saw that a key tool for solving systems efficiently was the use of matrices. In this chapter, we will finally give a proper definition of what, exactly, a matrix is, after which we will proceed to develop the algebraic properties of matrices, just as we did for vectors in Chapter 2.
A fundamental topic of mathematics is arithmetic; adding, subtracting, multiplying and dividing numbers. After learning how to do this, most of us went on to learn how to add, subtract, multiply and divide “\(x\)”. We are comfortable with expressions such as
This chapter deals with the idea of doing similar operations, but instead of an unknown number \(x\text{,}\) we will be using a matrix \(\tta\text{.}\) So what exactly does the expression
mean? Before we can do anything, we need to actually define what a matrix is! Once we’ve taken care of that, we are going to need to learn to define what matrix addition, scalar multiplication, matrix multiplication and matrix inversion are. We will learn just that, plus some more good stuff, in this chapter.
