Explanation Given: The invertible matrix is, A = [ 1 − 1 0 1 0 − 1 6 − 2 − 3 ] The message is, OWLS ARE NOCTURNAL Approach: To convert the coded message into uncoded row matrices with n entries, convert the message into numbers and partition the number, 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 use for the blank space. To encode a message, multiply each uncoded row matrices with the encoded matrix. Calculation: Partition of the message into the group of three produces the uncoded row matrices, [ 15 23 12 ] [ 19 0 1 ] [ 18 5 0 ] [ 14 15 3 ] [ 20 21 18 ] [ 14 1 12 ] Multiply the matrix uncoded row matrix [ 15 23 12 ] with encoded matrix A . [ 15 23 12 ] [ 1 − 1 0 1 0 − 1 6 − 2 − 3 ] = [ 110 − 39 − 59 ] Multiply the matrix uncoded row matrix [ 19 0 1 ] with encoded matrix A . [ 19 0 1 ] [ 1 − 1 0 1 0 − 1 6 − 2 − 3 ] = [ 25 − 21 − 3 ] Multiply the matrix uncoded row matrix [ 18 5 0 ] with encoded matrix A . [ 18 5 0 ] [ 1 − 1 0 1 0 − 1 6 − 2 − 3 ] = [ 23 − 18 − 5 ] Multiply the matrix uncoded row matrix [ 14 15 3 ] with encoded matrix A . [ 14 15 3 ] [ 1 − 1 0 1 0 − 1 6 − 2 − 3 ] = [ 47 − 20 − 24 ] Multiply the matrix uncoded row matrix [ 20 21 18 ] with encoded matrix A

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ISBN: 9781337271073

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 8.5, Problem 9CP

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The encode message OWLS ARE NOCTURNAL by using the encoded matrix A=[1−1010−16−2−3].

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Chapter 8.5, Problem 8CP

Chapter 8.5, Problem 10CP

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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

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The encode message OWLS ARE NOCTURNAL by using the encoded matrix A = [ 1 − 1 0 1 0 − 1 6 − 2 − 3 ] .

Solution Summary: The author explains how to convert the encoded message into uncoded row matrices with n entries.

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The encode message OWLS ARE NOCTURNAL by using the encoded matrix A=[1−1010−16−2−3].

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Chapter 8 Solutions