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:
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:
The number
a_{12} is the number in the
1st row and the
2nd
column. Thus,
a_{12} = 16.
a_{21} is the number in the
2nd
row and the
1st column. Thus,
a_{21} = - 12.
a_{11} = 1
a_{12} = 16
a_{21} = - 12
a_{22} = -
a_{31} = 4
a_{32} = 0
Matrix Addition
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:
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:
For example,