Explanation Given Information: Billy Sean after deciding his program gets to know that the University Senate has revised the bulletin and added a ‘Verbal Expression’ course replacing the Fine arts course in all programs: For the degree of Bachelor of Science the candidate must select a total of 120 credits from the Verbal Expression, Sciences, Liberal Arts and Mathematics. There should be an equal number of Science and Liberal Arts credits. There should be twice the number of verbal expression credits than the Science and Liberal Arts credits summed together. The Liberal Arts credits should exceed the Mathematics credits by one fourth of the number of Verbal Expression credits. Formula Used: Elementary row operations: Type 1: Replacing the row R i by a R i , where a is a nonzero number. Type 2: Replacing the row R i by a R i ± b R j , where a is a nonzero number. Gauss Jordan reduction method: Step 1: First clear the fractions or decimals if any. Step 2: Pivot the first nonzero element of the first row. Step 3: Use the pivot to clear its column. Step 4: Pivot the first nonzero element in the second row and clear the column. Step 5: Pivot the first nonzero element in the third row and clear the column. Step 6: Turn all the pivot elements into a 1. Calculation: Firstly identify and label the unknowns. Considering the provided information the unknowns should be labelled like this, x represents the number of credits of liberal arts y represents the number of credits of sciences z represents the number of credits of Verbal Expression w represents the number of credits of Mathematics It is known that he can select a total of 120 credits from all the subjects combined. x + y + z + w = 120 Also, there are an equal number of science and Liberal arts credits, x = y x − y = 0 Now, we are provided that the number of Verbal Expression credits is twice the sum of science and Liberal arts credits, which can be represented in the form of equation as, z = 2 ( x + y ) 2 x + 2 y − z = 0 From the information provided we know that Liberal Arts credits exceed the mathematics credits by one fourth the number of Verbal arts credits. This can be written in the form of equation as, x − w = 1 4 z x − 1 4 z − w = 0 The augmented matrix for the obtained equations is: [ 1 1 1 1 120 1 − 1 0 0 0 2 2 − 1 0 0 4 0 − 1 / 4 − 1 0 ] Apply Gauss Jordan reduction method to get the solution of the given system of equation. Begin by clearing the fraction in the rows of the matrix by the operation R 4 → 4 R 4 [ 1 1 1 1 120 1 1 0 0 0 2 2 − 1 0 0 4 1 − 1 / 4 − 1 0 ] → [ 1 1 1 1 120 1 − 1 0 0 0 2 2 − 1 0 0 4 0 − 1 − 4 0 ] Now, pivot the first nonzero element of first row and clear its column Perform the operation R 2 → R 2 − R 1 , R 3 → R 3 − 2 R 1 , [ 1 1 1 1 120 1 − 1 0 0 0 2 2 − 1 0 0 4 0 − 1 − 4 0 ] → [ 1 1 1 1 120 0 − 2 − 1 − 1 − 120 0 0 − 3 − 2 − 240 4 0 − 1 − 4 0 ] Further perform the operation R 4 → R 4 − 4 R 1 [ 1 1 1 1 120 0 − 2 − 1 − 1 − 120 0 0 − 3 − 2 − 240 4 0 − 1 − 4 0 ] → [ 1 1 1 1 120 0 − 2 − 1 − 1 − 120 0 0 − 3 − 2 − 240 0 − 4 − 5 − 8 − 480 ] Now, pivot the first nonzero element of second row and clear its column Perform the operation R 1 → 2 R 1 + R 2 , R 4 → R 4 − 2 R 2 , [ 1 1 1 1 120 0 − 2 − 1 − 1 − 120 0 0 − 3 − 2 − 240 0 − 4 − 5 − 8 − 480 ] → [ 2 0 1 1 120 0 − 2 − 1 − 1 − 120 0 0 − 3 − 2 − 240 0 0 − 3 − 6 − 240 ] Further simplify the fourth row by the operation R 4 → 1 3 R 4 [ 2 0 1 1 120 0 − 2 − 1 − 1 − 120 0 0 − 3 − 2 − 240 0 0 − 3 − 6 − 240 ] → [ 2 0 1 1 120 0 − 2 − 1 − 1 − 120 0 0 − 3 − 2 − 240 0 0 − 1 − 2 − 80 ] Now, select the first nonzero element of third row and clear its column

Finite Mathematics and Application Calculus (Looseleaf) - Text Only

7th Edition

ISBN: 9781337291484

Author: Waner

Publisher: Cengage

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Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.

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Chapter 4, Problem 42RE

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Chapter 4, Problem 41RE

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Chapter 4 Solutions

Finite Mathematics and Application Calculus (Looseleaf) - Text Only

Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...

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The possible combination of credits for Billy-Sean if the candidate must select a total of 120 credits from the Verbal Expression, Sciences, Liberal Arts and Mathematics.

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