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. 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.
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. 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.
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.3: M X N Matrices
Problem 49PS
Related questions
Question

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.

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

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 6 images

Recommended textbooks for you

Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning

Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning


Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning

Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning


Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning

Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning

College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning