Explanation Calculation: Consider, the matrix A = 1 2 2 3 7 9 − 1 − 4 − 7 and the cryptogram 13 − 9 − 59 61 112 106 − 17 − 73 − 131 11 24 29 65 144 172 . Use the elementary row operations to compute A − 1 , as A ⋮ I ⇒ I ⋮ A − 1 . Write the augmented matrix A with the identity matrix of order 3 × 3 , A ⋮ I = 1 2 2 3 7 9 − 1 − 4 − 7 ⋮ ⋮ ⋮ 1 0 0 0 1 0 0 0 1 Apply the row operations to reduce matrix A to I , Make the elements below the leading element of the first column 0 by multiplying row R 1 by − 3 and adding the result to R 2 . Multiply row R 1 by 1 and add the result to R 3 , − 3 R 1 + R 2 → R 1 + R 3 → 1 2 2 0 1 3 0 − 2 − 5 ⋮ ⋮ ⋮ 1 0 0 − 3 1 0 1 0 1 Make the elements below the leading element of the second column 0 by multiplying row R 2 by 2 and adding the result to R 3 , 2 R 2 + R 3 → 1 2 2 0 1 3 0 0 1 ⋮ ⋮ ⋮ 1 0 0 − 3 1 0 − 5 2 1 Make the elements above the leading element of the third column 0 by multiplying row R 3 by − 3 and adding the result to R 2 , − 3 R 3 + R 2 → 1 2 2 0 1 0 0 0 1 ⋮ ⋮ ⋮ 1 0 0 12 − 5 − 3 − 5 2 1 Make the elements above the leading element of the third column 0 by multiplying row R 3 by − 2 and adding the result to R 1 , − 2 R 3 + R 1 → 1 2 0 0 1 0 0 0 1 ⋮ ⋮ ⋮ 11 − 4 − 2 12 − 5 − 3 − 5 2 1 Make the elements above the leading element of the second column 0 by multiplying row R 2 by 4 3 and adding the result to R 1 , − 2 R 2 + R 1 → 1 0 0 0 1 0 0 0 1 ⋮ ⋮ ⋮ − 13 6 4 12 − 5 − 3 − 5 2 1 The above matrix becomes I ⋮ A − 1

10th Edition

ISBN: 9781337282291

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 7.5, Problem 58E

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To calculate: The decoded message of the cryptogram 13 −9 −59 61 112 106 −17 −73 −131 11 24 29 65 144 172, by using A−1 if, the matrix A=122379−1−4−7.

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Chapter 7 Solutions

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The decoded message of the cryptogram 13 − 9 − 59 61 112 106 − 17 − 73 − 131 11 24 29 65 144 172 , by using A − 1 if, the matrix A = 1 2 2 3 7 9 − 1 − 4 − 7 .

Solution Summary: The author calculates the decoded message of the provided cryptogram, "RETURN AT DAWN" by using A-1 if the matrix A=left[begin

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To calculate: The decoded message of the cryptogram 13 −9 −59 61 112 106 −17 −73 −131 11 24 29 65 144 172, by using A−1 if, the matrix A=122379−1−4−7.

Chapter 7 Solutions