Linear algebra Prof. El-Henawy
Elementary Matrices
Elementary Matrices and Nonelementary Matrices
Applications of Matrix Operations • Stochastic Matrices An n×n matrix P is called a stochastic matrix if each entry is a number between 0 and 1 and each column of P adds up to 1.
Examples of Stochastic Matrices and Nonstochastic Matrices
A Consumer Preference Model Two competing companies offer cable television service to a city of 100,000 households. The changes in cable subscriptions each year are shown in Figure 1. Company A now has 15,000 subscribers and Company B has 20,000 subscribers. How many subscribers will each company have 1 year from now?
A Consumer Preference Model
Figure 1
Cryptography A cryptogram is a message written according to a secret code (the Greek word kryptos means “hidden�). This section describes a method of using matrix multiplication to encode and decode messages. Begin by assigning a number to each letter in the alphabet (with 0 assigned to a blank space), as follows.
Example
Decoding a Message
Least Squares Regression line
Least Squares Regression Analysis
The sum of squared error for this line can be shown to be 0.8.