Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Chapter 10.3, Problem 27E
To determine

The solution of given system of linear equations having unique solutions using Gaussian elimination or gauss-Jordan elimination.

Expert Solution & Answer
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Answer to Problem 27E

The solution for given system of linear equation is.

Explanation of Solution

Given:

Equation given,

  2x−3y−z=13−x+2y−5z=65x−y−z=49

Concept Used:

Calculation:

Consider first the given equations,

  2x−3y−z=13−x+2y−5z=65x−y−z=49

Step1:

In the first step first convert the given, equation into augmented matrix.

  [2−3−113−12−565−1−149]

Step 2:

In the second step convert the augmented matrix into row echelon form.

For this row operation is performed. In the first row operation,

Perform,

  Row1/2=NewRow1

  Row1/2=[1−1.5−0.56.5−12−565−1−149]

  Row2+Row1=NewRow2

  Row2+Row1=[1−1.5−0.56.500.5−5.512.551149]

Now the next row operation to be performed is,

  Row2*2=NewRow2

  Row2*2= [11.5−0.56.500.511255−1149]

next row operation to be performed is,

  Row3−5*Row1=NewRow3

  [5−7.5−2.532.501112551149]

  15*Row1=[1515−3090152030−25−530−1045] and

  Row2−15*Row1=[11260560−115−530−1045]

  =NewRow2

Step3:

In the step 3 again perform row operations,

First perform,

  Row3+5*Row1

  =NewRow3

  Row3+5*Row1=[55−10300560−115−530−1045]

And,

  Row3+5*Row1=[11−2605601150352075]

  =NewRow3

Step 4:

The next step for row operation is,

  Row3−7*Row2=NewRow3

  7*Row2=[11−26035420805035−20755]

And,

  Row3−7*Row2=[11−260560−80500−440880] = NewRow3

Step4:

In this the matrix is in row echloen form,

Divide

  Row3/−440

And,

  Row2/5

  =[11−260112−23001−2]

Now the matrix is obtained in the row echelon form , write the equations from the matrix,

  x+y−2z=6 ….. (1)

  y+12z=−23 ….. (2)

  z=−2 ..... (3)

Step5:

In the step 5 values of x,y,z can be found using back substitution,From equation

Conclusion:

Hence, the solution for given system is (3,1,2)

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Chapter 10.3, Problem 26E
Next
Chapter 10.3, Problem 28E

Chapter 10 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 10.1 - The system of equations {2x+3y=75xy=9 is a system...Ch. 10.1 - Prob. 2ECh. 10.1 - A system of two linear equations in two variables...Ch. 10.1 - The following is a system of two linear equations...Ch. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10E
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Admission Fees The admission fee at an amusement...Ch. 10.1 - Gas Station A gas station sells regular gas for...Ch. 10.1 - Fruit Stand A fruit stand sells two varieties of...Ch. 10.1 - Airplane Speed A man flies a small airplane from...Ch. 10.1 - Boat Speed A boat on a river travels downstream...Ch. 10.1 - Nutrition A researcher performs an experiment to...Ch. 10.1 - Coffee Blends A customer in a coffee shop...Ch. 10.1 - Mixture Problem A chemist has two large containers...Ch. 10.1 - Mixture Problem A biologist has two brine...Ch. 10.1 - Investments A woman invests a total of 20,000 in...Ch. 10.1 - Investments A man invests his savings in two...Ch. 10.1 - Prob. 71ECh. 10.1 - Prob. 72ECh. 10.1 - Prob. 73ECh. 10.1 - Area of a Triangle Find the area of the triangle...Ch. 10.1 - Prob. 75ECh. 10.2 - These exercises refer to the following system:...Ch. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - 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Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
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