We have looked at several types of systems of equations and inequalities, and the methods for solving them. You can think of a system as groups of numbers that are ordered in a specific way. They are used to organize information, such as the number of pounds of each type of cheese used in a mixture.
Another way to order information is in a matrix. In a matrix, each row represents specific types of items and each column represents specific types of items.
The matrix below represents the makeup of a class of 3rd graders. The teacher took a poll to see which hand students typically used for writing or for other daily tasks. Then the teacher organized the results in this matrix.
You can see that each row represents either female or male students. There are columns to represent left-handed, right-handed, or ambidextrous students.
A matrix is a rectangular arrangementof numbers enclosed by brackets. It is used to organize information.
A matrix is usually identified by a capital letter, such as matrix A or B.
The rows are horizontal.
The columns are vertical.
The dimensions are represented in this way: # rows x # columns.
The elements are the numbers in the matrix.
The position of an element is identified by naming its row and column.
The plural of matrix is matrices.
Example 1: Parts of a Matrix
Let’s call this matrix A.
Identify each of the following in the matrix:
The number of rows.
The number of columns.
The dimensions of A.
The elements of A.
What is the position of the element zero in Matrix A?
two rows
three columns
dimensions 2 X 3 (read as 2 by 3)
The elements are: 0, 1, 2, 10, and 12.
The position of zero is row 2, column 3.
Quick Practice
Organize the following information into a matrix.
The Stationary R Us store is making orders for different types of items.
The Cartoon Series: 20 sets of letter paper, 15 sets of note cards, and 20 sets of envelopes.
The Floral Series: 32 sets of letter paper, 10 sets of note cards, and 15 sets of envelopes.
There are two ways you can organize the information.
Way 1: You could use the cartoon series for row 1 and the floral series for row 2 creating a 2 x 3 matrix. Notice that each column is the same type of item ordered: sets of letter paper are in column 1, sets of note cards are in column 2, and sets of envelopes are in column 3.
Way 2: You could use the cartoon series for column 1 and the floral series for column 2 creating a 3 x 2 matrix. Notice that each row is the same type of item ordered: sets of letter paper are in row 1, sets of note cards are in row 2, and sets of envelopes are in row 3.
The matrix below is an incorrect way to organize the information. Even though row 1 is for the cartoon series and row 2 is for the the floral series, the items in the columns do not match. For instance, the 15 in the first row, first column represents 15 sets of Notecards, but the 32 in the second row, first column represents the 32 sets of letter paper.
What are the dimensions of the following matrices?
1 X 2 3 X 3 3 X 2
In the matrix for problem 2b, which element is in the second row, thrd column?
A matrix is a rectangular arrangement of numbers enclosed by brackets. It is used to organize information. 
