Explanation Given information: The given equations are 3 x − y = 4 and 7 x + 2 y = 18 . Calculation: Use the given Equations and form matrix A . Express matrix A as follows: A = [ 3 − 1 7 2 ] Interchange the elements on the principal diagonal and change the signs of the off–diagonal elements. A changed = [ 2 1 − 7 3 ] Calculate the determinant value of matrix A . | A | = | 3 − 1 7 2 | = ( 3 × 2 ) − ( 7 × − 1 ) = 6 + 7 = 13 Calculate the inverse value of matrix A using the relation. A − 1 = A changed | A | Substitute [ 2 1 − 7 3 ] for A changed and 13 for | A | . A − 1 = [ 2 1 − 7 3 ] 13 = [ 2 13 1 13 − 7 13 3 13 ] Express the matrix C as follows: C = [ 4 18 ] Calculate the value of x and y using the relation. A − 1 C = [ x y ] Substitute [ 2 13 1 13 − 7 13 3 13 ] for A − 1 and [ 4 18 ] for C

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 16.4, Problem 17E

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Find the required solutions of x and y using the inverse of the coefficient matrix and the check the answer using calculator.

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Chapter 16.4, Problem 16E

Chapter 16.4, Problem 18E

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Chapter 16 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 16.1 - For matrices A and B, find A + B. Ch. 16.1 - Prob. 2PE Ch. 16.1 - Prob. 3PE Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E

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