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Introduction to Matrices
What is a matrix? What can a matrix be used for?

A matrix 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.

A =

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 as a12 (the element in the first row, second column) or a22 (the element in the second row, second column).

In our example a12 = 6 and a22 = 9.

Example Group #1
Consider the following matrix:

B =

Example What is the dimension of B?
What is your answer?
 
Example
What is the value of the element b13
What is your answer?
 
Example
What is the value of the element b21
What is your answer?
 

Example Group #2
Use matrices C and D given below to answer the next series of questions.

C =    D =

Example
What are the dimensions of each matrix?
What is your answer?
 
Example
What is the value of these elements: c21 and c32
What is your answer?
 
Example
What is the value of these elements: d32 and d34
What is your answer?
 
Example
Two matrices are considered equal, or equivalent, only if they have the same dimensions and every element is identical.

Find a matrix presented earlier in this lesson that is equivalent to E where E = .
What is your answer?
 



S Taylor

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