Explanation Calculation: Consider the matrix, A = 1 − 1 0 1 0 − 1 6 − 2 − 3 . And the cryptogram is, 110 − 39 − 59 25 − 21 − 3 23 − 18 − 5 47 − 20 − 24 149 − 56 − 75 87 − 38 − 37 . Use the elementary row operations to compute A − 1 as A ⋮ I = I ⋮ A − 1 . Write the augmentation of the matrix A with the identity matrix of order 3 × 3 , A ⋮ I = 1 − 1 0 1 0 − 1 6 − 2 − 3 ⋮ ⋮ ⋮ 1 0 0 0 1 0 0 0 1 Apply the row operations to reduce matrix A to I , Make the elements below the leading element of the first column 0 by multiplying row 1 by − 1 and adding the result to row 2 . Then, multiply row 1 by − 6 and add the result to row 3 as shown, − 1 R 1 + R 2 → − 6 R 1 + R 3 → 1 − 1 0 0 1 − 1 0 4 − 3 ⋮ ⋮ ⋮ 1 0 0 − 1 1 0 − 6 0 1 Add row 2 to row 1 and add − 4 of row 2 to row 3 , R 2 + R 1 → − 4 R 2 + R 3 → 1 0 − 1 0 1 − 1 0 0 1 ⋮ ⋮ ⋮ 0 1 0 − 1 1 0 − 2 − 4 1 Add row 3 to row 1 and row 2 , R 3 + R 1 → R 3 + R 2 → 1 0 0 0 1 0 0 0 1 ⋮ ⋮ ⋮ − 2 − 3 1 − 3 − 3 1 − 2 − 4 1 The above matrix results in I ⋮ A − 1 . Therefore, the inverse of the matrix A is A − 1 = − 2 − 3 1 − 3 − 3 1 − 2 − 4 1 . Now, divide the cryptogram into groups of three to form the coded row matrices, 110 − 39 − 59 25 − 21 − 3 23 − 18 − 5 47 − 20 − 24 149 − 56 − 75 87 − 38 − 37 Obtain the decoded matrices for the coded row matrices by multiplying coded row matrices by the matrix A − 1 = − 2 − 3 1 − 3 − 3 1 − 2 − 4 1

10th Edition

ISBN: 9781337282291

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 7.5, Problem 10ECP

To determine

To calculate: The decoded message of the cryptogram 110−39−5925−21−323−18−547−20−24149−56−7587−38−37 using the inverse of the matrix A=1−1010−16−2−3.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.5, Problem 9ECP

Chapter 7.5, Problem 1E

Students have asked these similar questions

Determine the multiplicative inverse of 11 in Z24. Your final answer should be an element of {0, 1, 2,..., 23}. Explain your answer.

Your friend sends a Whatapps message in hexadecimal, but you received it in decimal after being encrypted by the system. When you read the message, it shows "48,879". Determine what exactly this message means.

Calculate 19992 – 19982 + 19972 – 19962 + -22 + 12. ...

Chapter 7 Solutions

College Algebra

Ch. 7.1 - Determine the dimension of the matrix 14710238.Ch. 7.1 - Prob. 2ECP Ch. 7.1 - Identify the elementary row operation performed to...Ch. 7.1 - Compare solving the linear system below to solving...Ch. 7.1 - Determine whether the matrix is in row-echelon...Ch. 7.1 - Solve the system 3x+5y+3z=193x+4y+4z=84x8y6z=26.Ch. 7.1 - Prob. 7ECP Ch. 7.1 - Prob. 8ECP Ch. 7.1 - Solve the system 2x6y+6z=462x3y=31.Ch. 7.1 - Prob. 1E

Knowledge Booster

$Algebra$

Learn more about

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

The decoded message of the cryptogram 110 − 39 − 59 25 − 21 − 3 23 − 18 − 5 47 − 20 − 24 149 − 56 − 75 87 − 38 − 37 using the inverse of the matrix A = 1 − 1 0 1 0 − 1 6 − 2 − 3 .

Solution Summary: The author explains how to calculate the decoded message of the cryptogram .

Concept explainers

Videos

To calculate: The decoded message of the cryptogram 110−39−5925−21−323−18−547−20−24149−56−7587−38−37 using the inverse of the matrix A=1−1010−16−2−3.

Want to see the full answer?

Chapter 7 Solutions