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 a
12 (the
element in the first row, second column) or a
22 (the
element in the second row, second column).
In our example a
12 = 6 and a
22 = 9.