Explanation Calculation: Consider the matrix, A = 3 − 4 2 0 2 1 4 − 5 3 and the cryptogram is 112 − 140 83 19 − 25 13 72 − 76 61 95 − 118 71 20 21 38 35 − 23 36 42 − 48 32 . Use elementary row operations to compute A − 1 , as, A ⋮ I ⇒ I ⋮ A − 1 . Write the augmentation of matrix A with the identity matrix of order 3 × 3 , A ⋮ I = 3 − 4 2 0 2 1 4 − 5 3 ⋮ ⋮ ⋮ 1 0 0 0 1 0 0 0 1 Apply row operations to reduce matrix A to I , Make the leading entry of column 1 to 1 , multiply row R 1 by 1 3 , 1 3 R 1 → 1 − 4 3 2 3 0 2 1 4 − 5 3 ⋮ ⋮ ⋮ 1 3 0 0 0 1 0 0 0 1 Make the elements below the leading element of the first column 0 ; multiply row R 1 by − 4 and add the result to R 3 , − 4 R 1 + R 3 → 1 − 4 3 2 3 0 2 1 0 1 3 1 3 ⋮ ⋮ ⋮ 1 3 0 0 0 1 0 − 4 3 0 1 Make the leading entry of column 2 to 1 , multiply row R 2 by 1 2 , 1 2 R 2 → 1 − 4 3 2 3 0 1 1 2 0 1 3 1 3 ⋮ ⋮ ⋮ 1 3 0 0 0 1 2 0 − 4 3 0 1 Make the elements below the leading element of the second column 0 ; multiply row R 2 by − 1 3 and add the result to R 3 , − 1 3 R 2 + R 3 → 1 − 4 3 2 3 0 1 1 2 0 0 1 6 ⋮ ⋮ ⋮ 1 3 0 0 0 1 2 0 − 4 3 − 1 6 1 Make the leading entry of column 3 to 1 , multiply row R 3 by 6 , 6 R 3 → 1 − 4 3 2 3 0 1 1 2 0 0 1 ⋮ ⋮ ⋮ 1 3 0 0 0 1 2 0 − 8 − 1 6 Make the elements above the leading element of the third column 0 ; multiply row R 3 by − 1 2 and add the result to R 2 , − 1 2 R 3 + R 2 → 1 − 4 3 2 3 0 1 0 0 0 1 ⋮ ⋮ ⋮ 1 3 0 0 4 1 − 3 − 8 − 1 6 Make the elements above the leading element of the third column 0 ; multiply row R 3 by − 2 3 and add the result to R 1 , − 2 3 R 3 + R 1 → 1 − 4 3 0 0 1 0 0 0 1 ⋮ ⋮ ⋮ 17 3 2 3 − 4 4 1 − 3 − 8 − 1 6 Make the elements above the leading element of the second column 0 ; multiply row R 2 by 4 3 and add the result to R 1 , 4 3 R 2 + R 1 → 1 0 0 0 1 0 0 0 1 ⋮ ⋮ ⋮ 11 2 − 8 4 1 − 3 − 8 − 1 6 The above matrix results in I ⋮ A − 1

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ISBN: 8220103599528

Author: Larson

Publisher: CENGAGE L

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Chapter 7.5, Problem 56E

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To calculate: The decoded message of the cryptogram, 112 −140 83 19 −25 13 72 −76 61 95 −118 71 20 21 38 35 −23 36 42 −48 32, by using A−1 if, the matrix is A=3−420214−53.

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Chapter 7.5, Problem 55E

Chapter 7.5, Problem 57E

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Chapter 7 Solutions

EBK COLLEGE ALGEBRA

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The decoded message of the cryptogram, 112 − 140 83 19 − 25 13 72 − 76 61 95 − 118 71 20 21 38 35 − 23 36 42 − 48 32 , by using A − 1 if, the matrix is A = 3 − 4 2 0 2 1 4 − 5 3 .

Solution Summary: The author calculates the decoded message of the cryptogram by using A-1 if the matrix is A=left[cc

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To calculate: The decoded message of the cryptogram, 112 −140 83 19 −25 13 72 −76 61 95 −118 71 20 21 38 35 −23 36 42 −48 32, by using A−1 if, the matrix is A=3−420214−53.

Want to see the full answer?

Chapter 7 Solutions

The decoded message of the cryptogram, 112 ​ − 140 83 19 − 25 13 72 − 76 61 95 − 118 71 ​ 20 21 38 35 − 23 36 42 − 48 32 , by using A − 1 if, the matrix is A = 3 − 4 2 0 2 1 4 − 5 3 .

Solution Summary: The author calculates the decoded message of the cryptogram by using A-1 if the matrix is A=left[cc

Videos

To calculate: The decoded message of the cryptogram, 112 ​−140 83 19 −25 13 72 −76 61 95 −118 71​ 20 21 38 35 −23 36 42 −48 32, by using A−1 if, the matrix is A=3−420214−53.

Want to see the full answer?

Chapter 7 Solutions

The decoded message of the cryptogram, 112 − 140 83 19 − 25 13 72 − 76 61 95 − 118 71 20 21 38 35 − 23 36 42 − 48 32 , by using A − 1 if, the matrix is A = 3 − 4 2 0 2 1 4 − 5 3 .

To calculate: The decoded message of the cryptogram, 112 −140 83 19 −25 13 72 −76 61 95 −118 71 20 21 38 35 −23 36 42 −48 32, by using A−1 if, the matrix is A=3−420214−53.