### Matrices

The SparkNote section on Ordered Pairs explained how to represent data as an ordered pair. Another way to represent data is in a matrix. An m×n matrix has m rows and n columns, and each entry is given a unique name, based on its row and column:

 A =   The matrix A is often denoted [A].

The number of rows and the number of columns are called dimensions. Here is an example of a 3×2-dimensional matrix:

 A =   The number a12 is the number in the 1st row and the 2nd column. Thus, a12 = 16. a21 is the number in the 2nd row and the 1st column. Thus, a21 = - 12.

a11 = 1
a12 = 16
a21 = - 12
a22 = - a31 = 4
a32 = 0

Two matrices can be added if and only if they have the same number of rows and the same number of columns. To add two matrices, add their corresponding entries:

 [A] + [B] =   +   =   For example,   +   =   =   Matrix addition is commutative: A + B = B + A. Matrix addition is also associative: (A + B) + C = A + (B + C).

### Matrix Subtraction

As in addition, two matrices can be subtracted if and only if they have the same number of rows and the same number of columns. To subtract one matrix from another, subtract their corresponding entries:

 [A] - [B] =   -   =   For example,   -   =   =   