Explanation Given: The encoded matrix is, A = [ 1 2 2 3 7 9 − 1 − 4 − 7 ] The cryptogram is, 20 17 − 15 − 12 − 56 − 104 1 − 25 − 65 62 143 181 Approach: To decode the message multiply each coded matrix formed from cryptogram with the inverse of encoding matrix. To find the inverse of matrix A is write the matrix as augmented matrix, [ A ⋮ I ] If the matrix is invertible then, matrix can be reduced as, [ I ⋮ A − 1 ] Here, I is the identity matrix. 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. Calculation: The augmented matrix is, [ 1 2 2 1 0 0 3 7 9 0 1 0 − 1 − 4 − 7 0 0 1 ] Apply the row operation R 2 → R 2 − 3 R 1 and R 3 → R 3 + R 1 . [ 1 2 2 1 0 0 0 1 3 − 3 1 0 0 − 2 − 5 1 0 1 ] Apply the row operation R 1 → R 1 − 2 R 2 and R 3 → R 3 + 2 R 2 . [ 1 0 − 4 7 − 2 0 0 1 3 − 3 1 0 0 0 1 − 5 2 1 ] Apply the row operation R → R 1 + 4 R 3 and R 2 → R 2 − 3 R 3 . [ 1 0 0 − 13 6 4 0 1 3 12 − 5 − 3 0 0 1 − 5 2 1 ] Thus, the inverse of the matrix is, A − 1 = [ − 13 6 4 12 − 5 − 3 − 5 2 1 ] Partition of the cryptogram into the group of three produces the coded row matrices, [ 20 17 − 15 ] [ − 12 − 56 − 104 ] [ 1 − 25 − 65 ] [ − 62 143 181 ] Multiply the coded row matrix [ 20 17 − 15 ] with A − 1

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Author: Ron Larson

Publisher: Cengage Learning

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Chapter 8.5, Problem 57E

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To decode:

The cryptogram by using the inverse of A.

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Chapter 8.5, Problem 56E

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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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To decode: The cryptogram by using the inverse of A .

Solution Summary: The author explains how to decode the cryptogram by using the inverse of A.

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To decode:

The cryptogram by using the inverse of A.

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Chapter 8 Solutions

To decode: The cryptogram by using the inverse of A .

Solution Summary: The author explains how to decode the cryptogram by using the inverse of A.

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To decode: The cryptogram by using the inverse of A.

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Chapter 8 Solutions

To decode:

The cryptogram by using the inverse of A.