 # Introduction to Matrices

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Videos, worksheets, games and activities to help Algebra students learn about matrices and how they can be used.

What is a Matrix?
A matrix is a rectangular array of variables or constants in horizontal rows and vertical columns, usually enclosed in brackets.
Each value in a matrix is called an element.
The dimensions of a matrix is the size of the matrix measured in rows and columns.

A row matrix is a matrix with only one row.
A column matrix is a matrix with only column row.
A square matrix is a matrix with the same number of rows as columns.
A zero matrix is a matrix in which every element is zero..
Equal matrices have the same dimensions and each element is equal.

Multiplying Matrices
The following diagram shows how to multiply two matrices. Scroll down the page for more examples of multiplying matrices and other matrix operations. Introduction to Matrices
Example:
Sharon wants to install cable television in her new apartment. There are two cable companies in the area whose prices are listed below. Use a matrix to organize the information. When is each company's service less expensive? Operations with Matrices
If A and B are two m × n matrices, then A + B is an m &time; n matrix in which each element is the sum of the corresponding elements of A and B.

Subtraction of Matrices
If A and B are two m × n matrices, then A - B is an m &time; n matrix in which each element is the difference of the corresponding elements of A and B.

Scalar Multiplication
The product of a scalar k and an m × n matrix is an m × n matrix in which each element equals k times the corresponding elements of the original matrix.

How to multiply two matrices?
You can only multiply two matrices if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix.
The element aij of AB is the sum of the products of the corresponding elements in row i of A and column j of B.
Examples:
1. Determine whether each matrix product is defined, If so, state the dimensions of the product.
a) A2 × 5 and B5 × 4
b) A1 × 3 and B4 × 3

2. In a four-team track meet, 5 points were awarded for each first-place finish, 3 pints for each second, and 1 point for each third. Find the total number of points for each school. Which school won the meet? What a matrix is?
How to add and subtract them?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  