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Math Algebra Algebra and Trigonometry

(a) Explain how Gaussian elimination works. (b) Use Gaussian elimination to put the following system in triangular form, and then solve the system. System Triangular form { x + y − 2 z = 3 x + 2 y + z = 5 3 x − y + 5 z = 1

(a) Explain how Gaussian elimination works. (b) Use Gaussian elimination to put the following system in triangular form, and then solve the system. System Triangular form { x + y − 2 z = 3 x + 2 y + z = 5 3 x − y + 5 z = 1

Solution Summary: The author explains the Gaussian elimination method and how it can be used to convert a linear equation into an equivalent triangular system.

Algebra and Trigonometry

Algebra and Trigonometry

4th Edition

ISBN: 9781305719781

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: PEARSON

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Textbook Question

Chapter 10.CR, Problem 6CC

(a) Explain how Gaussian elimination works.

(b) Use Gaussian elimination to put the following system in triangular form, and then solve the system.

System	Triangular form
{ x + y − 2 z = 3 x + 2 y + z = 5 3 x − y + 5 z = 1

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Chapter 10.CR, Problem 5CC

Chapter 10.CR, Problem 7CC

Chapter 10 Solutions

Algebra and Trigonometry

Ch. 10.1 - CONCEPTS The system of equations {2x+3y=75xy=9 is...Ch. 10.1 - CONCEPTS A system of equations in two variables...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - SKILLS 58 Substitution Method Use the...Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - SKILLS 1314 Graphical MethodTwo equations and...Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - SKILLS 1520 Number of Solutions Determined...Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - 2150 Solving a System of Equations Solve the...Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - 2150 Solving a System of Equations Solve the...Ch. 10.1 - 2150 Solving a System of Equations Solve the...Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - 21-50Solving a system of linear equationsSolve the...Ch. 10.1 - 21-50Solving a system of linear equationsSolve the...Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - 21-50Solving a system of linear equationsSolve the...Ch. 10.1 - Prob. 44E Ch. 10.1 - Prob. 45E Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - Prob. 48E Ch. 10.1 - 2150 Solving a System of Equations Solve the...Ch. 10.1 - Prob. 50E Ch. 10.1 - Prob. 51E Ch. 10.1 - Prob. 52E Ch. 10.1 - Prob. 53E Ch. 10.1 - Prob. 54E Ch. 10.1 - SKILLS Plus 55-58 Solving a General System of...Ch. 10.1 - Prob. 56E Ch. 10.1 - Prob. 57E Ch. 10.1 - Prob. 58E Ch. 10.1 - Prob. 59E Ch. 10.1 - Prob. 60E Ch. 10.1 - APPLICATIONS Value of Coins A man has 14 coins in...Ch. 10.1 - Prob. 62E Ch. 10.1 - Prob. 63E Ch. 10.1 - Prob. 64E Ch. 10.1 - Prob. 65E Ch. 10.1 - Prob. 66E Ch. 10.1 - Nutrition A researcher performs an experiment to...Ch. 10.1 - Prob. 68E Ch. 10.1 - Prob. 69E Ch. 10.1 - Mixture problem A biologist has two brine...Ch. 10.1 - Prob. 71E Ch. 10.1 - Prob. 72E Ch. 10.1 - APPLICATIONS Distance, Speed, and Time John and...Ch. 10.1 - Prob. 74E Ch. 10.1 - Prob. 75E Ch. 10.1 - Prob. 76E Ch. 10.1 - Prob. 77E Ch. 10.2 - 1-2these exercises refer to the following system:...Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - SKILLS 7-12Triangular SystemsUse back-substitution...Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - SKILLS 13-16Eliminating a VariablePerform an...Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 15E Ch. 10.2 - Prob. 16E Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E Ch. 10.2 - SKILLS 17-38Solving a System of Equations in Three...Ch. 10.2 - Prob. 20E Ch. 10.2 - Prob. 21E Ch. 10.2 - SKILLS 17-38Solving a System of Equations in Three...Ch. 10.2 - Prob. 23E Ch. 10.2 - Prob. 24E Ch. 10.2 - SKILLS 17-38Solving a System of Equations in Three...Ch. 10.2 - Prob. 26E Ch. 10.2 - Prob. 27E Ch. 10.2 - Prob. 28E Ch. 10.2 - Prob. 29E Ch. 10.2 - Prob. 30E Ch. 10.2 - SKILLS 17-38Solving a System of Equations in Three...Ch. 10.2 - Prob. 32E Ch. 10.2 - Prob. 33E Ch. 10.2 - Prob. 34E Ch. 10.2 - Prob. 35E Ch. 10.2 - Prob. 36E Ch. 10.2 - SKILLS 17-38Solving a System of Equations in Three...Ch. 10.2 - Prob. 38E Ch. 10.2 - APPLICATIONS Financial PlanningMark has 100,000 to...Ch. 10.2 - Prob. 40E Ch. 10.2 - APPLICATIONS AgricultureA farmer has 1200 acres of...Ch. 10.2 - Gas Station A gas station sells three types of...Ch. 10.2 - Nutrition A biologist is performing an experiment...Ch. 10.2 - Prob. 44E Ch. 10.2 - APPLICATIONS Juice Blends The Juice Company offers...Ch. 10.2 - Prob. 46E Ch. 10.2 - APPLICATIONS Stock Portfolio An investor owns...Ch. 10.2 - Electricity By using Kirchhoffs Laws, it can be...Ch. 10.2 - Prob. 49E Ch. 10.3 - Prob. 1E Ch. 10.3 - Prob. 2E Ch. 10.3 - Prob. 3E Ch. 10.3 - Prob. 4E Ch. 10.3 - Prob. 5E Ch. 10.3 - Prob. 6E Ch. 10.3 - Prob. 7E Ch. 10.3 - Prob. 8E Ch. 10.3 - Prob. 9E Ch. 10.3 - Prob. 10E Ch. 10.3 - Prob. 11E Ch. 10.3 - Prob. 12E Ch. 10.3 - Prob. 13E Ch. 10.3 - Prob. 14E Ch. 10.3 - Prob. 15E Ch. 10.3 - Prob. 16E Ch. 10.3 - Prob. 17E Ch. 10.3 - Prob. 18E Ch. 10.3 - Prob. 19E Ch. 10.3 - Prob. 20E Ch. 10.3 - Prob. 21E Ch. 10.3 - Prob. 22E Ch. 10.3 - Prob. 23E Ch. 10.3 - Prob. 24E Ch. 10.3 - Prob. 25E Ch. 10.3 - Prob. 26E Ch. 10.3 - Prob. 27E Ch. 10.3 - Prob. 28E Ch. 10.3 - Prob. 29E Ch. 10.3 - Prob. 30E Ch. 10.3 - Prob. 31E Ch. 10.3 - Prob. 32E Ch. 10.3 - Prob. 33E Ch. 10.3 - Prob. 34E Ch. 10.3 - Prob. 35E Ch. 10.3 - Prob. 36E Ch. 10.3 - Prob. 37E Ch. 10.3 - Prob. 38E Ch. 10.3 - Prob. 39E Ch. 10.3 - Prob. 40E Ch. 10.3 - Prob. 41E Ch. 10.3 - Prob. 42E Ch. 10.3 - Prob. 43E Ch. 10.3 - Prob. 44E Ch. 10.3 - Prob. 45E Ch. 10.3 - Prob. 46E Ch. 10.3 - Prob. 47E Ch. 10.3 - Prob. 48E Ch. 10.4 - CONCEPTS 1-2The system of equations {2yx2=0yx=4 is...Ch. 10.4 - Prob. 2E Ch. 10.4 - Prob. 3E Ch. 10.4 - Prob. 4E Ch. 10.4 - Prob. 5E Ch. 10.4 - Prob. 6E Ch. 10.4 - SKILLS 3-8Substitution MethodUse the substitution...Ch. 10.4 - Prob. 8E Ch. 10.4 - Prob. 9E Ch. 10.4 - Prob. 10E Ch. 10.4 - Prob. 11E Ch. 10.4 - SKILLS 9-14Elimination MethodUse the elimination...Ch. 10.4 - SKILLS 9-14Elimination MethodUse the elimination...Ch. 10.4 - Prob. 14E Ch. 10.4 - Prob. 15E Ch. 10.4 - SKILLS 15-18Finding Intersection Points...Ch. 10.4 - Prob. 17E Ch. 10.4 - Prob. 18E Ch. 10.4 - SKILLS 19-32Solving Nonlinear SystemsFind all...Ch. 10.4 - Prob. 20E Ch. 10.4 - Prob. 21E Ch. 10.4 - Prob. 22E Ch. 10.4 - Prob. 23E Ch. 10.4 - Prob. 24E Ch. 10.4 - SKILLS 19-32Solving Nonlinear SystemsFind all...Ch. 10.4 - SKILLS 19-32Solving Nonlinear SystemsFind all...Ch. 10.4 - Prob. 27E Ch. 10.4 - Prob. 28E Ch. 10.4 - Prob. 29E Ch. 10.4 - Prob. 30E Ch. 10.4 - SKILLS 19-32Solving Nonlinear SystemsFind all...Ch. 10.4 - Prob. 32E Ch. 10.4 - Prob. 33E Ch. 10.4 - Prob. 34E Ch. 10.4 - Prob. 35E Ch. 10.4 - Prob. 36E Ch. 10.4 - SKILLS 33-40Graphical MethodUse the graphical...Ch. 10.4 - Prob. 38E Ch. 10.4 - Prob. 39E Ch. 10.4 - Prob. 40E Ch. 10.4 - Prob. 41E Ch. 10.4 - Prob. 42E Ch. 10.4 - SKILLS Plus 41-44Some Tricker SystemsFollow the...Ch. 10.4 - Prob. 44E Ch. 10.4 - Prob. 45E Ch. 10.4 - Prob. 46E Ch. 10.4 - Prob. 47E Ch. 10.4 - Prob. 48E Ch. 10.4 - APPLICATIONS Flight of a RocketA hill is inclined...Ch. 10.4 - Prob. 50E Ch. 10.4 - Global Positioning System GPS The Global...Ch. 10.4 - Prob. 52E Ch. 10.5 - Prob. 1E Ch. 10.5 - Prob. 2E Ch. 10.5 - Prob. 3E Ch. 10.5 - Prob. 4E Ch. 10.5 - Prob. 5E Ch. 10.5 - Prob. 6E Ch. 10.5 - Prob. 7E Ch. 10.5 - Prob. 8E Ch. 10.5 - Prob. 9E Ch. 10.5 - Prob. 10E Ch. 10.5 - Prob. 11E Ch. 10.5 - Prob. 12E Ch. 10.5 - Prob. 13E Ch. 10.5 - Prob. 14E Ch. 10.5 - Prob. 15E Ch. 10.5 - Prob. 16E Ch. 10.5 - Prob. 17E Ch. 10.5 - Prob. 18E Ch. 10.5 - Prob. 19E Ch. 10.5 - Prob. 20E Ch. 10.5 - Prob. 21E Ch. 10.5 - Prob. 22E Ch. 10.5 - Prob. 23E Ch. 10.5 - Prob. 24E Ch. 10.5 - Prob. 25E Ch. 10.5 - Prob. 26E Ch. 10.5 - Prob. 27E Ch. 10.5 - Prob. 28E Ch. 10.5 - Prob. 29E Ch. 10.5 - Prob. 30E Ch. 10.5 - Prob. 31E Ch. 10.5 - Prob. 32E Ch. 10.5 - Prob. 33E Ch. 10.5 - Prob. 34E Ch. 10.5 - Prob. 35E Ch. 10.5 - Prob. 36E Ch. 10.5 - Prob. 37E Ch. 10.5 - Prob. 38E Ch. 10.5 - Prob. 39E Ch. 10.5 - Prob. 40E Ch. 10.5 - Prob. 41E Ch. 10.5 - Prob. 42E Ch. 10.5 - Prob. 43E Ch. 10.5 - Prob. 44E Ch. 10.5 - Prob. 45E Ch. 10.5 - Prob. 46E Ch. 10.5 - Prob. 47E Ch. 10.5 - Prob. 48E Ch. 10.5 - Prob. 49E Ch. 10.5 - Prob. 50E Ch. 10.5 - Prob. 51E Ch. 10.5 - Prob. 52E Ch. 10.5 - Prob. 53E Ch. 10.5 - Prob. 54E Ch. 10.5 - Prob. 55E Ch. 10.5 - Prob. 56E Ch. 10.5 - Prob. 57E Ch. 10.5 - Prob. 58E Ch. 10.5 - Prob. 59E Ch. 10.5 - Prob. 60E Ch. 10.5 - Prob. 61E Ch. 10.5 - Prob. 62E Ch. 10.5 - Prob. 63E Ch. 10.5 - Prob. 64E Ch. 10.5 - Prob. 65E Ch. 10.5 - Prob. 66E Ch. 10.5 - Prob. 67E Ch. 10.5 - Prob. 68E Ch. 10.5 - Prob. 69E Ch. 10.5 - Prob. 70E Ch. 10.5 - Prob. 71E Ch. 10.5 - Prob. 72E Ch. 10.5 - APPLICATIONS Coffee BlendsA coffee merchant sells...Ch. 10.5 - Prob. 74E Ch. 10.5 - Prob. 75E Ch. 10.CR - Prob. 1CC Ch. 10.CR - Prob. 2CC Ch. 10.CR - What is a system of linear equations in the...Ch. 10.CR - For a system of two linear equations in two...Ch. 10.CR - What operations can be performed on a linear...Ch. 10.CR - aExplain how Gaussian elimination works. bUse...Ch. 10.CR - Prob. 7CC Ch. 10.CR - Prob. 8CC Ch. 10.CR - Prob. 9CC Ch. 10.CR - Prob. 1E Ch. 10.CR - Prob. 2E Ch. 10.CR - Prob. 3E Ch. 10.CR - Prob. 4E Ch. 10.CR - Prob. 5E Ch. 10.CR - Prob. 6E Ch. 10.CR - Prob. 7E Ch. 10.CR - Prob. 8E Ch. 10.CR - Prob. 9E Ch. 10.CR - Prob. 10E Ch. 10.CR - Prob. 11E Ch. 10.CR - Prob. 12E Ch. 10.CR - Prob. 13E Ch. 10.CR - Prob. 14E Ch. 10.CR - Prob. 15E Ch. 10.CR - Prob. 16E Ch. 10.CR - Prob. 17E Ch. 10.CR - Prob. 18E Ch. 10.CR - Prob. 19E Ch. 10.CR - Prob. 20E Ch. 10.CR - Prob. 21E Ch. 10.CR - Prob. 22E Ch. 10.CR - Prob. 23E Ch. 10.CR - Prob. 24E Ch. 10.CR - Prob. 25E Ch. 10.CR - Prob. 26E Ch. 10.CR - Prob. 27E Ch. 10.CR - Prob. 28E Ch. 10.CR - Prob. 29E Ch. 10.CR - Prob. 30E Ch. 10.CR - Prob. 31E Ch. 10.CR - Prob. 32E Ch. 10.CR - Prob. 33E Ch. 10.CR - Prob. 34E Ch. 10.CR - Prob. 35E Ch. 10.CR - Prob. 36E Ch. 10.CR - Prob. 37E Ch. 10.CR - Prob. 38E Ch. 10.CR - Prob. 39E Ch. 10.CR - Prob. 40E Ch. 10.CR - Prob. 41E Ch. 10.CR - Prob. 42E Ch. 10.CR - Prob. 43E Ch. 10.CR - Prob. 44E Ch. 10.CR - Prob. 45E Ch. 10.CR - Prob. 46E Ch. 10.CR - Prob. 47E Ch. 10.CR - Prob. 48E Ch. 10.CR - Prob. 49E Ch. 10.CR - Prob. 50E Ch. 10.CR - Prob. 51E Ch. 10.CR - Prob. 52E Ch. 10.CR - Prob. 53E Ch. 10.CR - Prob. 54E Ch. 10.CR - Prob. 55E Ch. 10.CR - Prob. 56E Ch. 10.CR - Prob. 57E Ch. 10.CR - Prob. 58E Ch. 10.CT - Prob. 1CT Ch. 10.CT - Prob. 2CT Ch. 10.CT - Prob. 3CT Ch. 10.CT - Prob. 4CT Ch. 10.CT - Prob. 5CT Ch. 10.CT - Prob. 6CT Ch. 10.CT - Prob. 7CT Ch. 10.CT - Prob. 8CT Ch. 10.CT - In 212h an airplane travels 600km against the...Ch. 10.CT - Prob. 10CT Ch. 10.CT - Prob. 11CT Ch. 10.CT - Prob. 12CT Ch. 10.CT - Prob. 13CT Ch. 10.CT - Prob. 14CT Ch. 10.CT - Prob. 15CT Ch. 10.CT - Prob. 16CT Ch. 10.FOM - PROBLEMS 1-4Find the maximum and minimum values of...Ch. 10.FOM - 1-4 Find the maximum and the minimum values of the...Ch. 10.FOM - 1-4 Find the maximum and minimum values of the...Ch. 10.FOM - Prob. 4P Ch. 10.FOM - Making FurnitureA furniture manufacturer makes...Ch. 10.FOM - A Housing DevelopmentA housing contractor has...Ch. 10.FOM - Prob. 7P Ch. 10.FOM - Manufacturing Calculators A manufacturer of...Ch. 10.FOM - Shipping TelevisionsAn electronics discount chain...Ch. 10.FOM - Prob. 10P Ch. 10.FOM - Prob. 11P Ch. 10.FOM - Prob. 12P Ch. 10.FOM - Investing in BondsA woman wishes to invest 12,000...Ch. 10.FOM - Prob. 14P Ch. 10.FOM - Business StrategyA small software company...Ch. 10.FOM - Feasible RegionAll parts of this problem refer to...

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