Chapter 2 Systems of Linear Equations and Matrices

1 / 16

# Chapter 2 Systems of Linear Equations and Matrices - PowerPoint PPT Presentation

Chapter 2 Systems of Linear Equations and Matrices. Section 2.4 Multiplication of Matrices. Writing Systems of Equations in Abbreviated Form. Consider the following system of equations with three unknowns. 2x + y – z = 2 x + 3y + 2z = 1 x + y + z = 2

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Chapter 2 Systems of Linear Equations and Matrices' - gwylan

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Chapter 2Systems of Linear Equations and Matrices

Section 2.4

Multiplication of Matrices

Writing Systems of Equations in Abbreviated Form
• Consider the following system of equations with three unknowns.

2x + y – z = 2

x + 3y + 2z = 1

x + y + z = 2

This system can be written in an abbreviated

form as

What is a Matrix?
• A matrix is a rectangular array of numbers enclosed by brackets.
• Each number in the array is an element or entry.
• An augmented matrix separates the constants in the last column of the matrix from the coefficients of the variables with a vertical line.
Classifications of Matrices
• Often named with capital letters.
• Classified by size (the number of rows and columns they contain).
• A matrix with m rows and n columns is an m x n matrix. The number of rows is always given first.
Special Types of Matrices
• A matrix with the same number of rows as columns is called a square matrix.
• A matrix containing only one row is called a row matrix or a row vector.
• A matrix of only one column is a column matrix or a column vector.
Scalar Multiplication
• When determining the product of a real number and a matrix, the real number is called a scalar.
Example
• Find the product of each of the following.

1.) -5A 2.) 2B

Notice that when you multiply a 2 X 3 matrix with a 3 X 1 matrix, the product is a 2 X 1 matrix.

CAUTION!!!
• Sometimes the product of two matrices does not exist!
• The product AB of two matrices A and B can be found only if the number of columns of A is the same as the number of rows of B.
• The final product will have as many rows as A and as many columns of B.
Examples for Us!

Use the matrices defined above to find the following

products, if they exist.

1.) AF 2.) AC 3.) DE

4.) ED 5.) BD 6.) EA