0.2 Matrices

Chapter overview

In this chapter, you will learn to:

1. Do matrix operations.
2. Solve linear systems using the Gauss-Jordan method.
3. Solve linear systems using the matrix inverse method.
4. Do application problems.

Introduction to matrices

Section overview

In this section you will learn to:

1. Add and subtract matrices.
2. Multiply a matrix by a scalar.
3. Multiply two matrices.

A matrix is a rectangular array of numbers. Matrices are useful in organizing and manipulating large amounts of data. In order to get some idea of what matrices are all about, we will look at the following example.

Before we go any further, we need to familiarize ourselves with some terms that are associated with matrices. The numbers in a matrix are called the entries or the elements of a matrix. Whenever we talk about a matrix, we need to know the size or the dimension of the matrix. The dimension of a matrix is the number of rows and columns it has. When we say a matrix is a 3 by 4 matrix, we are saying that it has 3 rows and 4 columns. The rows are always mentioned first and the columns second. This means that a $3\times 4$ matrix does not have the same dimension as a $4\times 3$ matrix. A matrix that has the same number of rows as columns is called a square matrix . A matrix with all entries zero is called a zero matrix . A square matrix with 1's along the main diagonal and zeros everywhere else, is called an identity matrix . When a square matrix is multiplied by an identity matrix of same size, the matrix remains the same. A matrix with only one row is called a row matrix or a row vector , and a matrix with only one column is called a column matrix or a column vector . Two matrices are equal if they have the same size and the corresponding entries are equal.