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7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337280426

Chapter 4.3, Problem 65E

Textbook Problem

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**Encryption** *Matrices are commonly used to encrypt data. Here is a simple form such an encryption can take. First, we represent each letter in the alphabet by a number, so let us take <space>*

*To encrypt this coded phrase, we use an invertible matrix of any size with integer entries. For instance, let us take A to be the*
*matrix*
*We can first arrange the coded sequence of numbers in the form of a matrix with two rows (using zero in the last place if we have an odd number of characters) and then multiply on the left by A:*

* Encrypted matrix*

*Which we can also write as*

*To decipher the encoded message, multiply the encrypted matrix by*
*Exercises 63–66 use the above matrix A for encoding and decoding.*

Decode the following message, which was encrypted using the matrix *A*.

To determine

**To calculate:** The decoded form of the message *A* where

**Given Information:**

Each letter in the alphabet is represented by a number, and the sequence of numbers is arranged in the form of a matrix with two rows and the sequence is multiplied on the left by *A* where

**Formula used:**

A matrix with *m* rows and *n* columns is of dimension *m* and *n* are positive integers.

**Calculation:**

Consider the encoded message,

Write as a matrix with two rows as below,

To calculate the decoded message, multiply the inverse of the matrix *A* by the encoded message.

Thus, decoded message is

Since, number of rows in

Since, number of rows in

Since, number of columns in

Finite Mathematics

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In Exercises 1720, write the given system of...Ch. 4 - In Exercises 1720, write the given system of...Ch. 4 - In Exercises 2124, solve the game with the given...Ch. 4 - In Exercises 2124, solve the game with the given...Ch. 4 - In Exercises 2124, solve the game with the given...Ch. 4 - In Exercises 2124, solve the game with the given...Ch. 4 - In Exercises 2528, find the production vector X...Ch. 4 - In Exercises 2528, find the production vector X...Ch. 4 - In Exercises 2528, find the production vector X...Ch. 4 - In Exercises 2528, find the production vector X...Ch. 4 - It is now July 1, and online sales of romance,...Ch. 4 - It is now July 1, and online sales of romance,...Ch. 4 - It is now July 1, and online sales of romance,...Ch. 4 - It is now July 1, and online sales of romance,...Ch. 4 - It is now July 1, and online sales of romance,...Ch. 4 - It is now July 1, and online sales of romance,...Ch. 4 - Acting on a tip from Marjory Duffin, John OHagan...Ch. 4 - Acting on a tip from Marjory Duffin, John OHagan...Ch. 4 - Acting on a tip from Marjory Duffin, John OHagan...Ch. 4 - Acting on a tip from Marjory Duffin, John OHagan...Ch. 4 - OHaganBooks.com has two main...Ch. 4 - OHaganBooks.com has two main...Ch. 4 - OHaganBooks.com has two main...Ch. 4 - OHaganBooks.com has two main...Ch. 4 - Publisher Marjory Duffin reveals that...Ch. 4 - Publisher Marjory Duffin reveals that...Ch. 4 - Publisher Marjory Duffin reveals that...Ch. 4 - Publisher Marjory Duffin reveals that...Ch. 4 - Publisher Marjory Duffin reveals that...Ch. 4 - Publisher Marjory Duffin reveals that...Ch. 4 - Some of the books sold by OHaganBooks.com are...Ch. 4 - Some of the books sold by OHaganBooks.com are...Ch. 4 - Some of the books sold by OHaganBooks.com are...Ch. 4 - Some of the books sold by OHaganBooks.com are...

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Probability and Statistics for Engineering and the Sciences

For Problems 11-14, find the absolute value. 73

Intermediate Algebra

Prove that if (a,b,c) is a Pythagorean triple and n is a natural number, the (na,nb,nc) is also a Pythagorean t...

Elementary Geometry For College Students, 7e

Write the sum in expanded form. 3. i=463i

Single Variable Calculus: Early Transcendentals

PUTNAM EXAM CHALLENGE Find the minimum value of | sinx=cosx+tanx+cotx+secx+cscx | for real numbers x. This prob...

Calculus of a Single Variable

According to moncy.CNN.com. with mortguge rates near 35-year lows, you may he able to cut your payments sharply...

Contemporary Mathematics for Business & Consumers

21. Let be the principal ideal . Determine whether each of the following polynomials is an element of .
a. b....

Elements Of Modern Algebra

Softball Diamond In softball, the distance from home plate to first base is 60 feet, as is the distance from fi...

Trigonometry (MindTap Course List)

In Exercises 1-8, list the simple events associated with the experiment. Quality Control As a part of quality c...

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 17 to 22, factor completely. 3y2+24y+45

Elementary Geometry for College Students

Finding Points of Intersection In Exercises 101 and 102, find the points of intersection of the graphs of the e...

Calculus: Early Transcendental Functions (MindTap Course List)

Add the following expressions. 3a11d8ma+11d3m

Mathematics For Machine Technology

The graph of x = 2 + 3t, y = 4 − t is a:
circle
ellipse
line
parabola

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Solve each equation for y and graph the equation. Then check your graph with a graphing calculator. y3x=6

College Algebra (MindTap Course List)

The point plotted at the right has coordinates:
(2, 5, 4)
(5, 2, 4)
(4, 2, 5)
(2, 4, 5)

Study Guide for Stewart's Multivariable Calculus, 8th

Finding Moments of Inertia and Radii of Gyration In Exercises 3538, find Ix,Iy,I0,x and y for the lamina bounde...

Calculus (MindTap Course List)

A study reported in the Journal of Small Business Management concluded that self-employed individuals do not ex...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

A study investigated the relationship between audit delay (Delay), the length of time from a companys fiscal ye...

Statistics for Business & Economics, Revised (MindTap Course List)

A researcher plans to select a sample from each of the following populations. Which is likely to be a probabili...

Research Methods for the Behavioral Sciences (MindTap Course List)

A tropical forest survey conducted by Conservation International included the following statements in the mater...

Introduction To Statistics And Data Analysis

Describe the nonexpenmental pretest-posttest design and the quasi-experimental time-series design, and identify...

Research Methods for the Behavioral Sciences (MindTap Course List)