Explanation Given: The encoded matrix is, A = [ 1 2 3 5 ] The cryptogram is, 11 21 64 112 25 50 29 53 23 46 40 75 55 92 Approach: To decode the message multiply each coded matrix formed from cryptogram with the inverse of encoding matrix. The inverse of 2 × 2 matrix A = [ a b c d ] is, A − 1 = 1 a d − b c [ d − b − c a ] The number that represents each letter is the place it comes in the alphabetical sequence starting from A as number 1 to Z as number 26. 0 is used for the blank space. Calculation: The inverse of the encoding matrix A is, A − 1 = 1 ( 1 ( 5 ) − 2 ( 3 ) ) [ 5 − 2 − 3 1 ] = − 1 [ 5 − 2 − 3 1 ] = [ − 5 2 3 − 1 ] Partition of the cryptogram into the group of two produces the coded row matrices, [ 11 21 ] [ 64 112 ] [ 25 50 ] [ 29 53 ] [ 23 46 ] [ 40 75 ] [ 55 92 ] Multiply the coded row matrix [ 11 21 ] with A − 1 . [ 11 21 ] [ − 5 2 3 − 1 ] = [ 8 1 ] Multiply the coded row matrix [ 64 112 ] with A − 1 . [ 64 112 ] [ − 5 2 3 − 1 ] = [ 16 16 ] Multiply the coded row matrix [ 25 50 ] with A − 1

10th Edition

ISBN: 9781337271073

Author: Ron Larson

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Videos

Question

Chapter 8.5, Problem 53E

To determine

The decoded message with A−1.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.5, Problem 52E

Chapter 8.5, Problem 54E

Students have asked these similar questions

Decoding Messages Use the numerical representation from Exercise 40 and the inverse of the encodingfunction C(x) = 3x + 2 to decode 41 5 35 17 83 4177 83 14 5 77.

Linear algebra: please show all steps correctly and handwritten

Mathematics: Linear Algebra 1) A firm uses three types of raw materials plastic, wood, and metal in the production of two products P1 and P2. The number of units of plastic, wood, and metal used for each unit of P1 are: 3, 2 and 4, respectively, and for each unit of P2 are 4, 1, and 3, respectively. Suppose the firm produces 20 units of P1 and 30 units of P2 each week. Express the answers to the following questions as matrix products. a. What is the weekly consumption of the three raw materials? b. If the unit costs (in €) for plastic, wood, and metal are 6, and 12, respectively, what are the costs of raw materials per unit of P1 and P2? C. What is the total amount spent on raw materials per week on the production of P1 and P2? 2) A building contractor can purchase the required lumber, bricks, concrete, glass, and paint from any one of three suppliers. The prices that each supplier charges for each unit of these five materials are given in matrix A. A Matrices = ܣ ܩ ܩ 545 756 2 41 5 25…

Chapter 8 Solutions

Precalculus (MindTap Course List)

Ch. 8.1 - Prob. 1CP Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Prob. 5CP Ch. 8.1 - Prob. 6CP Ch. 8.1 - Prob. 7CP Ch. 8.1 - Prob. 8CP Ch. 8.1 - Prob. 9CP Ch. 8.1 - Prob. 1E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The decoded message with A − 1 .

Solution Summary: The author explains how to determine the decoded message with A-1. They multiply each encoded matrix with the inverse of encoding matrix.

Concept explainers

Videos

The decoded message with A−1.

Want to see the full answer?

Chapter 8 Solutions