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Matrix Operations Guide

This document discusses matrices and matrix multiplication. It defines what a matrix is, how they are classified by size and type, and how to perform scalar multiplication and matrix multiplication. Matrix multiplication can only be performed if the number of columns of the first matrix equals the number of rows of the second matrix. Examples are provided to demonstrate scalar and matrix multiplication.

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45 views16 pages

Matrix Operations Guide

This document discusses matrices and matrix multiplication. It defines what a matrix is, how they are classified by size and type, and how to perform scalar multiplication and matrix multiplication. Matrix multiplication can only be performed if the number of columns of the first matrix equals the number of rows of the second matrix. Examples are provided to demonstrate scalar and matrix multiplication.

Uploaded by

anup
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PPT, PDF, TXT or read online on Scribd
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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
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.

5 7
A

4 2
1.) -5A

4 2 2

B 6 3 8
1 5 12

2.)

2B

Matrix Multiplication

Example

Solution

Answer

Notice that when you multiply a 2 X 3


matrix with a 3 X 1 matrix, the product is
a 2 X 1 matrix.

Another Example

Solution

Answer

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

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