What is a matrix? What can a matrix
be used for?
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.
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
in the first row, second column) or a22
in the second row, second column).
In our example a12
= 6 and a22