Introduction to Matrices

What is a matrix? What can a matrix be used for?

A matrix is a rectangular array of numbers that has many uses. Some of these include solving systems of equations, storing data, and representing geometric transformations. An example of a matrix is shown below.

A =

Notice that this matrix has been labeled with a capital letter. This is a standard notation when working with matrices (matrices is the plural form of matrix).

This is an example of a matrix. There are two rows that go across and two columns that go down. This is called the dimension of the matrix.

The notation for the dimension of a matrix is dim(A) = . The first number always refers to the number of rows and the second number always refers to the number of columns. In this case, the rows and columns are the same, but we always have to be careful in writing the dimensions of a matrix to be sure to put rows followed by columns.

Since the rows and the columns are the same in matrix A, we can refer to it as a square matrix.

We can refer to a particular element in the matrix as a₁₂ (the element in the first row, second column) or a₂₂ (the element in the second row, second column).

In our example a₁₂ = 6 and a₂₂ = 9.