Algebra for College Students
Algebra for College Students
10th Edition
ISBN: 9781285195780
Author: Jerome E. Kaufmann, Karen L. Schwitters
Publisher: Cengage Learning
Bartleby Related Questions Icon

Related questions

Question
[画像:1. Cryptopgraphy (a) We wish to encode a message using a simple cipher and matrix multiplication. For the cipher, we will assign to the letters of the alphabet A B C ... Z the numbers 1,..., 26 corresponding to their position in the alphabet and the number 27 represents a blank space. The idea is to write the message as a m x nmatrix and then use an invertible mxm matrix and matrix multiplication to encode and decode the message. For example, we may write "PEACE" as the 2 x 3 matrix M by using the cipher and then grouping the numbers into 2 x 1 columns, thus M = 16 1 5 5 3 27 If we now take a 2 x 2 invertible matrix E as the encryption matrix, we may encrypt the message using matrix multiplication as EM. For example, if E= the message "PEACE", after the multiplication EM and 'unzipped' from the matrix becomes 54 53 - 26 - 34 42 The following message was encrypted using the matrix C where: 1 2 3 C 2 5 3 108 107 193 133 108 183 156 76 91 177 136 236 187 95 172 118 Decode this message. You can use software or a site such as matrixcalc.org to perform the calcula- tions, but you must clearly show your procedure. (b) Spy Headquarters sends a message to one of its agents using the encoding matrix The agent uses the matrix A = B = -(3) 3 5 (14) to send messages to their informers. Find the encoding matrix that is consistent with this commu- nication pathway that enable Headquarters to send messages directly to the informers. Show all of your work.]
expand button
Transcribed Image Text:1. Cryptopgraphy (a) We wish to encode a message using a simple cipher and matrix multiplication. For the cipher, we will assign to the letters of the alphabet A B C ... Z the numbers 1,..., 26 corresponding to their position in the alphabet and the number 27 represents a blank space. The idea is to write the message as a m x nmatrix and then use an invertible mxm matrix and matrix multiplication to encode and decode the message. For example, we may write "PEACE" as the 2 x 3 matrix M by using the cipher and then grouping the numbers into 2 x 1 columns, thus M = 16 1 5 5 3 27 If we now take a 2 x 2 invertible matrix E as the encryption matrix, we may encrypt the message using matrix multiplication as EM. For example, if E= the message "PEACE", after the multiplication EM and 'unzipped' from the matrix becomes 54 53 - 26 - 34 42 The following message was encrypted using the matrix C where: 1 2 3 C 2 5 3 108 107 193 133 108 183 156 76 91 177 136 236 187 95 172 118 Decode this message. You can use software or a site such as matrixcalc.org to perform the calcula- tions, but you must clearly show your procedure. (b) Spy Headquarters sends a message to one of its agents using the encoding matrix The agent uses the matrix A = B = -(3) 3 5 (14) to send messages to their informers. Find the encoding matrix that is consistent with this commu- nication pathway that enable Headquarters to send messages directly to the informers. Show all of your work.
[画像:1. Cryptopgraphy (a) We wish to encode a message using a simple cipher and matrix multiplication. For the cipher, we will assign to the letters of the alphabet A B C ... Z the numbers 1,..., 26 corresponding to their position in the alphabet and the number 27 represents a blank space. The idea is to write the message as a m x nmatrix and then use an invertible mxm matrix and matrix multiplication to encode and decode the message. For example, we may write "PEACE" as the 2 x 3 matrix M by using the cipher and then grouping the numbers into 2 x 1 columns, thus M = 16 1 5 5 3 27 If we now take a 2 x 2 invertible matrix E as the encryption matrix, we may encrypt the message using matrix multiplication as EM. For example, if E= the message "PEACE", after the multiplication EM and 'unzipped' from the matrix becomes 54 53 - 26 - 34 42 The following message was encrypted using the matrix C where: 1 2 3 C 2 5 3 108 107 193 133 108 183 156 76 91 177 136 236 187 95 172 118 Decode this message. You can use software or a site such as matrixcalc.org to perform the calcula- tions, but you must clearly show your procedure. (b) Spy Headquarters sends a message to one of its agents using the encoding matrix The agent uses the matrix A = B = -(3) 3 5 (14) to send messages to their informers. Find the encoding matrix that is consistent with this commu- nication pathway that enable Headquarters to send messages directly to the informers. Show all of your work.]
expand button
Transcribed Image Text:1. Cryptopgraphy (a) We wish to encode a message using a simple cipher and matrix multiplication. For the cipher, we will assign to the letters of the alphabet A B C ... Z the numbers 1,..., 26 corresponding to their position in the alphabet and the number 27 represents a blank space. The idea is to write the message as a m x nmatrix and then use an invertible mxm matrix and matrix multiplication to encode and decode the message. For example, we may write "PEACE" as the 2 x 3 matrix M by using the cipher and then grouping the numbers into 2 x 1 columns, thus M = 16 1 5 5 3 27 If we now take a 2 x 2 invertible matrix E as the encryption matrix, we may encrypt the message using matrix multiplication as EM. For example, if E= the message "PEACE", after the multiplication EM and 'unzipped' from the matrix becomes 54 53 - 26 - 34 42 The following message was encrypted using the matrix C where: 1 2 3 C 2 5 3 108 107 193 133 108 183 156 76 91 177 136 236 187 95 172 118 Decode this message. You can use software or a site such as matrixcalc.org to perform the calcula- tions, but you must clearly show your procedure. (b) Spy Headquarters sends a message to one of its agents using the encoding matrix The agent uses the matrix A = B = -(3) 3 5 (14) to send messages to their informers. Find the encoding matrix that is consistent with this commu- nication pathway that enable Headquarters to send messages directly to the informers. Show all of your work.
Expert Solution
Check Mark
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Text book image
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Text book image
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Text book image
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning