Explanation Given: A satellite company has A = 90 , 000 customers and a cable company has B = 85 , 000 customers this year. Procedure used: 1. Form an augmented matrix [ A | I ] where a matrix A is placed along with a same dimension identity matrix I separated by a line. 2. Apply row operations on [ A | I ] in order to obtain another augmented matrix [ I | B ] where I , is again an identity matrix and B is an inverse of A. 3. If the reduction process yields a row of zeros in the left half of the augmented matrix, then the inverse of A does not exist. Calculation: Take A = [ 2 3 2 5 1 3 3 5 ] and X = [ a b ] and transform [ 2 3 2 5 1 3 3 5 ] [ a b ] = [ 90 , 000 85 , 000 ] as follows. A − 1 A X = A − 1 [ 90 , 000 85 , 000 ] ( Multiply with A − 1 on RHS of both sides ) I X = A − 1 [ 90 , 000 85 , 000 ] ( ∵ A − 1 A = I ) X = A − 1 [ 90 , 000 85 , 000 ] Obtain the augmented matrix as follows. [ 2 3 2 5 1 0 1 3 3 5 0 1 ] Apply the row operation 15 R 1 → R 1 and 15 R 2 → R 2 and reduce the matrix. [ 10 6 15 0 5 9 0 15 ] Apply the row operation R 1 − 2 R 2 → R 2 and reduce the matrix

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Author: YOCCO

Publisher: Pearson Education (US)

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Chapter 7.4, Problem 26E

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To find: The matrix [ab] that represents the last year customers of two companies such that [35132523][ab]=[AB] gives the customers present this year.

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Chapter 7.4, Problem 25E

Chapter 7.4, Problem 27E

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Chapter 7 Solutions

EBK COLLEGE ALGEBRA IN CONTEXT

Ch. 7.1 - In Exercises 14, solve the systems of equations....Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

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The matrix [ a b ] that represents the last year customers of two companies such that [ 3 5 1 3 2 5 2 3 ] [ a b ] = [ A B ] gives the customers present this year.

Solution Summary: The author explains how the augmented matrix left[A|Iright] represents the last year customers of two companies.

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To find: The matrix [ab] that represents the last year customers of two companies such that [35132523][ab]=[AB] gives the customers present this year.

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Chapter 7 Solutions