Matrices are commonly used to encrypt data. Here is a simple form such encryption can take. First, we represent each letter in the alphabet by a number, so let us take 0, A 1, 8= 2, and so on. Thus, for example, "ABORT MISSION" becomes [1 2 15 18 20 0 13 9 19 19 9 15 14]. 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 2 x 2 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. 15 20 13 19 '9 14 2 18 0 9 19 15 0 63 60 48 76 42 42] 10 102 40 62 114 78 28] Encrypted Matrix= which we can also write as [5 10 63 102 60 40 48 62 76 114 42 78 42 28). To decipher the encoded message, multiply the encrypted matrix by A The following question uses the above matrix A for encoding and decoding. Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.) [24 66 72 108 18 22 60 40 17 58 80 130 33 82)
Matrices are commonly used to encrypt data. Here is a simple form such encryption can take. First, we represent each letter in the alphabet by a number, so let us take 0, A 1, 8= 2, and so on. Thus, for example, "ABORT MISSION" becomes [1 2 15 18 20 0 13 9 19 19 9 15 14]. 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 2 x 2 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. 15 20 13 19 '9 14 2 18 0 9 19 15 0 63 60 48 76 42 42] 10 102 40 62 114 78 28] Encrypted Matrix= which we can also write as [5 10 63 102 60 40 48 62 76 114 42 78 42 28). To decipher the encoded message, multiply the encrypted matrix by A The following question uses the above matrix A for encoding and decoding. Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.) [24 66 72 108 18 22 60 40 17 58 80 130 33 82)
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 51PS
Related questions
Question
![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> = 0, A = 1, B = 2, and so on. Thus, for example, "ABORT MISSION" becomes
[1 2 15 18 20 0 13 9 19 19 9 15 14].
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 2 x 2 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.
15 20 13 19 '9
14
Encrypted Matrix
2 18 0 9 19 15 0
63 60 48
76 42 42
10 102 40 62 114 78
28
which we can also write as
[5 10 63 102 60 40 48 62 76 114 42 78 42 28).
To decipher the encoded message, multiply the encrypted matrix by A. The following question uses the above matrix A for encoding and decoding.
Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.)
[24 66 72 108 18 22 60 40 17 58 80 130 33 82]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28cf2dea-71b7-4a9d-8a4b-5214354e17b1%2F1fa63516-5078-41f3-8d23-1714ce246693%2Fthqvll_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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> = 0, A = 1, B = 2, and so on. Thus, for example, "ABORT MISSION" becomes
[1 2 15 18 20 0 13 9 19 19 9 15 14].
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 2 x 2 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.
15 20 13 19 '9
14
Encrypted Matrix
2 18 0 9 19 15 0
63 60 48
76 42 42
10 102 40 62 114 78
28
which we can also write as
[5 10 63 102 60 40 48 62 76 114 42 78 42 28).
To decipher the encoded message, multiply the encrypted matrix by A. The following question uses the above matrix A for encoding and decoding.
Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.)
[24 66 72 108 18 22 60 40 17 58 80 130 33 82]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
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.Recommended textbooks for you
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
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
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning