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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.