Explanation Given information: The rate of interest of a first loan is 4.0 %. The rate of interest of a second loan is 3.0 %. The total amount for the two loans is $245. The annual interest is $290 if the second loan had been for twice as much. Calculation: Express the Equation for first loan as follows: 4.0 100 x + 3.0 100 y = 245 0.04 x + 0.03 y = 245 Express the Equation for second loan as follows: 4.0 100 x + 6.0 100 y = 290 0.04 x + 0.06 y = 290 Use the Equations and form matrix A . Express matrix A as follows: A = [ 0.04 0.03 0.04 0.06 ] Interchange the elements on the principal diagonal and change the signs of the off–diagonal elements. A changed = [ 0.06 − 0.03 − 0.04 0.04 ] Calculate the determinant value of matrix A . | A | = | 0.04 0.03 0.04 0.06 | = ( 0.04 × 0.06 ) − ( 0.04 × 0.03 ) = 0.0024 − 0.0012 = 0.0012 Calculate the inverse value of matrix A using the relation. A − 1 = A changed | A | Substitute [ 0.06 − 0.03 − 0.04 0.04 ] for A changed and 0.3 for | A | . A − 1 = [ 0.06 − 0.03 − 0.04 0.04 ] 0.0012 = [ 0.06 0.0012 − 0.03 0.0012 − 0.04 0.0012 0.04 0.0012 ] = [ 50 − 25 − 100 3 100 3 ] Express the matrix C as follows: C = [ 245 290 ] Calculate the value of x and y using the relation

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780135902912

Author: Allyn J. Washington

Publisher: PEARSON

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Chapter 16.4, Problem 36E

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Chapter 16.4, Problem 35E

Chapter 16.4, Problem 37E

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Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

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