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 10.2, Problem 18E
To determine

The complete solution of linear system or show that it is inconsistent.

Expert Solution & Answer
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Answer to Problem 18E

The solution for given system is (x,y,z)=(1,0,−1) .

Explanation of Solution

Given:

Equation given,

  x−y+z=0y+2z=−2x+y−z=2

Concept Used:

The concept of Gaussian elimination is used to concert the linear system into row echelon form.

Calculation:

Consider first the given equations,

  x−y+z=0 ….. (1)

  y+2z=−2 …… (2)

  x+y−z=2 …… (3)

Step1:

In the first step first to obtain a triangular system eliminate the variables x,y from Equation (3) .

Now first to eliminate x from Equation (3)

Multiply Equation (1) by (−1)

  (−1)*(x−y+z=0)=−x+y−z=0

Now, Add Equation (1) and Equation (3) .

  x−x+y+y+−z−z=2+0

The equation obtained can be written as

  2y−2z=2 ….New equation (3)

Step 2:

Now to eliminate y from the New equation (3)

Multiply equation (2) with (−2)

  −2*(y+2z=−2)−2y−4z=4

  −2y−4z=4 ….New equation (2)

Now, Add the New equation (2) and New equation (3) .

  −2y+2y+−4z+(−2)z=2+4

Thus the equation obtained is,

  −6z=6

The triangular system of equations can now be written as,

  x−y+z=0y+2z=−2−6z=6

From the last equation the value of z can be obtained,

  −6z=6z=−66z=−1z=−1

Substitute the value of z=−1 equation (2) to get the value of y ,

  y+2*(−1)=−2y−2=−2y=−2+2y=0

Substitute the value of y,z in equation (1) to get x

  x−y+z=0x−0+(−1)=0x−1=0x=0+1x=1x=1

Conclusion:

Hence, the solution for given system is (x,y,z)=(1,0,−1) .

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Chapter 10.2, Problem 17E
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Chapter 10.2, Problem 19E

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
Ch. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - Prob. 16ECh. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - Prob. 19ECh. 10.1 - Prob. 20ECh. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.1 - Prob. 32ECh. 10.1 - Prob. 33ECh. 10.1 - Prob. 34ECh. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - Prob. 37ECh. 10.1 - Prob. 38ECh. 10.1 - Prob. 39ECh. 10.1 - Prob. 40ECh. 10.1 - Prob. 41ECh. 10.1 - Prob. 42ECh. 10.1 - Prob. 43ECh. 10.1 - Prob. 44ECh. 10.1 - Prob. 45ECh. 10.1 - Prob. 46ECh. 10.1 - Prob. 47ECh. 10.1 - Prob. 48ECh. 10.1 - Prob. 49ECh. 10.1 - Prob. 50ECh. 10.1 - Prob. 51ECh. 10.1 - Prob. 52ECh. 10.1 - Prob. 53ECh. 10.1 - Prob. 54ECh. 10.1 - Prob. 55ECh. 10.1 - Prob. 56ECh. 10.1 - Prob. 57ECh. 10.1 - Prob. 58ECh. 10.1 - Value of Coins A man has 14 coins in his pocket,...Ch. 10.1 - 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 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - Prob. 28ECh. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Prob. 35ECh. 10.2 - Prob. 36ECh. 10.2 - Prob. 37ECh. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.2 - Gas Station A gas station sells three types of...Ch. 10.2 - Nutrition A biologist is performing an experiment...Ch. 10.2 - Diet Program Nicole started a new diet that...Ch. 10.2 - Juice Blends The Juice Company offers three kinds...Ch. 10.2 - Appliance Manufacturing Kitchen Korner produces...Ch. 10.2 - Stock Portfolio An investor owns three stocks: A,...Ch. 10.2 - Electricity By using Kirchhoffs Laws, it can be...Ch. 10.2 - Prob. 47ECh. 10.3 - If a system of linear equations has infinitely...Ch. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Prob. 12ECh. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Prob. 24ECh. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Prob. 43ECh. 10.3 - Prob. 44ECh. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - Prob. 48ECh. 10.3 - Prob. 49ECh. 10.3 - Prob. 50ECh. 10.3 - Prob. 51ECh. 10.3 - Prob. 52ECh. 10.3 - Prob. 53ECh. 10.3 - Prob. 54ECh. 10.3 - Nutrition A doctor recommends that a patient take...Ch. 10.3 - Mixtures A chemist has three acid solutions at...Ch. 10.3 - Distance, Speed, and Time Amanda, Bryce, and Corey...Ch. 10.3 - Classroom Use A small school has 100 students who...Ch. 10.3 - Manufacturing Furniture A furniture factory makes...Ch. 10.3 - Traffic Flow A section of a citys street network...Ch. 10.3 - Prob. 61ECh. 10.4 - We can add (or subtract) two matrices only if they...Ch. 10.4 - (a) We can multiply two matrices only if the...Ch. 10.4 - Prob. 3ECh. 10.4 - Fill in the missing entries in the product matrix....Ch. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - 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Prob. 8ECh. 10.5 - Prob. 9ECh. 10.5 - Prob. 10ECh. 10.5 - Prob. 11ECh. 10.5 - Prob. 12ECh. 10.5 - Prob. 13ECh. 10.5 - Prob. 14ECh. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 - Prob. 21ECh. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 - Prob. 26ECh. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - Prob. 32ECh. 10.5 - Prob. 33ECh. 10.5 - Prob. 34ECh. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Prob. 37ECh. 10.5 - Prob. 38ECh. 10.5 - Prob. 39ECh. 10.5 - Prob. 40ECh. 10.5 - Prob. 41ECh. 10.5 - Prob. 42ECh. 10.5 - Prob. 43ECh. 10.5 - Prob. 44ECh. 10.5 - Prob. 45ECh. 10.5 - Prob. 46ECh. 10.5 - Nutrition A nutritionist is studying the effects...Ch. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.5 - Prob. 50ECh. 10.6 - True or false? det(A) is defined only for a square...Ch. 10.6 - Prob. 2ECh. 10.6 - True or false? If det(A) = 0, then A is not...Ch. 10.6 - Prob. 4ECh. 10.6 - Prob. 5ECh. 10.6 - Prob. 6ECh. 10.6 - Prob. 7ECh. 10.6 - Prob. 8ECh. 10.6 - Prob. 9ECh. 10.6 - Prob. 10ECh. 10.6 - Prob. 11ECh. 10.6 - Prob. 12ECh. 10.6 - Prob. 13ECh. 10.6 - Prob. 14ECh. 10.6 - Prob. 15ECh. 10.6 - Prob. 16ECh. 10.6 - Prob. 17ECh. 10.6 - Prob. 18ECh. 10.6 - Prob. 19ECh. 10.6 - Prob. 20ECh. 10.6 - Prob. 21ECh. 10.6 - Prob. 22ECh. 10.6 - Prob. 23ECh. 10.6 - Prob. 24ECh. 10.6 - Prob. 25ECh. 10.6 - Prob. 26ECh. 10.6 - Prob. 27ECh. 10.6 - Prob. 28ECh. 10.6 - Prob. 29ECh. 10.6 - Prob. 30ECh. 10.6 - Prob. 31ECh. 10.6 - Prob. 32ECh. 10.6 - Prob. 33ECh. 10.6 - Prob. 34ECh. 10.6 - Prob. 35ECh. 10.6 - Prob. 36ECh. 10.6 - Prob. 37ECh. 10.6 - Prob. 38ECh. 10.6 - Prob. 39ECh. 10.6 - Prob. 40ECh. 10.6 - Prob. 41ECh. 10.6 - Prob. 42ECh. 10.6 - Prob. 43ECh. 10.6 - Prob. 44ECh. 10.6 - Prob. 45ECh. 10.6 - Prob. 46ECh. 10.6 - Prob. 47ECh. 10.6 - Prob. 48ECh. 10.6 - Prob. 49ECh. 10.6 - Prob. 50ECh. 10.6 - Prob. 51ECh. 10.6 - Prob. 52ECh. 10.6 - Prob. 53ECh. 10.6 - Prob. 54ECh. 10.6 - Prob. 55ECh. 10.6 - Prob. 56ECh. 10.6 - Prob. 57ECh. 10.6 - Prob. 58ECh. 10.6 - Prob. 59ECh. 10.6 - Prob. 60ECh. 10.6 - The Arch of a Bridge The opening of a railway...Ch. 10.6 - A Triangular Plot of Land An outdoors club is...Ch. 10.6 - Prob. 63ECh. 10.6 - Prob. 64ECh. 10.6 - Prob. 65ECh. 10.6 - Prob. 66ECh. 10.6 - Prob. 67ECh. 10.7 - For each rational function r, choose from (i)(iv)...Ch. 10.7 - Prob. 2ECh. 10.7 - Prob. 3ECh. 10.7 - Prob. 4ECh. 10.7 - Prob. 5ECh. 10.7 - Prob. 6ECh. 10.7 - Prob. 7ECh. 10.7 - Prob. 8ECh. 10.7 - Prob. 9ECh. 10.7 - Prob. 10ECh. 10.7 - Prob. 11ECh. 10.7 - Prob. 12ECh. 10.7 - Prob. 13ECh. 10.7 - Prob. 14ECh. 10.7 - Prob. 15ECh. 10.7 - Prob. 16ECh. 10.7 - Prob. 17ECh. 10.7 - Prob. 18ECh. 10.7 - Prob. 19ECh. 10.7 - Prob. 20ECh. 10.7 - Prob. 21ECh. 10.7 - Prob. 22ECh. 10.7 - Prob. 23ECh. 10.7 - Prob. 24ECh. 10.7 - Prob. 25ECh. 10.7 - Prob. 26ECh. 10.7 - Prob. 27ECh. 10.7 - Prob. 28ECh. 10.7 - Prob. 29ECh. 10.7 - Prob. 30ECh. 10.7 - Prob. 31ECh. 10.7 - Prob. 32ECh. 10.7 - Prob. 33ECh. 10.7 - Prob. 34ECh. 10.7 - Prob. 35ECh. 10.7 - Prob. 36ECh. 10.7 - Prob. 37ECh. 10.7 - Prob. 38ECh. 10.7 - Prob. 39ECh. 10.7 - Prob. 40ECh. 10.7 - Prob. 41ECh. 10.7 - Prob. 42ECh. 10.7 - Prob. 43ECh. 10.7 - Prob. 44ECh. 10.7 - Prob. 45ECh. 10.7 - Prob. 46ECh. 10.7 - Prob. 47ECh. 10.7 - Prob. 48ECh. 10.8 - The system of equations {2yx2=0yx=4 is graphed...Ch. 10.8 - Prob. 2ECh. 10.8 - Prob. 3ECh. 10.8 - Prob. 4ECh. 10.8 - Prob. 5ECh. 10.8 - Prob. 6ECh. 10.8 - Prob. 7ECh. 10.8 - Prob. 8ECh. 10.8 - Prob. 9ECh. 10.8 - Prob. 10ECh. 10.8 - Prob. 11ECh. 10.8 - Prob. 12ECh. 10.8 - Prob. 13ECh. 10.8 - Prob. 14ECh. 10.8 - Prob. 15ECh. 10.8 - Prob. 16ECh. 10.8 - Prob. 17ECh. 10.8 - Prob. 18ECh. 10.8 - Prob. 19ECh. 10.8 - Prob. 20ECh. 10.8 - Prob. 21ECh. 10.8 - Prob. 22ECh. 10.8 - Prob. 23ECh. 10.8 - Prob. 24ECh. 10.8 - Prob. 25ECh. 10.8 - Prob. 26ECh. 10.8 - Prob. 27ECh. 10.8 - Prob. 28ECh. 10.8 - Prob. 29ECh. 10.8 - Prob. 30ECh. 10.8 - Prob. 31ECh. 10.8 - Prob. 32ECh. 10.8 - Prob. 33ECh. 10.8 - Prob. 34ECh. 10.8 - Prob. 35ECh. 10.8 - Prob. 36ECh. 10.8 - Prob. 37ECh. 10.8 - Prob. 38ECh. 10.8 - Prob. 39ECh. 10.8 - Prob. 40ECh. 10.8 - Dimensions of a Rectangle A rectangle has an area...Ch. 10.8 - Legs of a Right Triangle A right triangle has an...Ch. 10.8 - Dimensions of a Rectangle The perimeter of a...Ch. 10.8 - Dimensions of a Rectangle A circular piece of...Ch. 10.8 - Flight of a Rocket A hill is inclined so that its...Ch. 10.8 - Making a Stovepipe A rectangular piece of sheet...Ch. 10.8 - Global Positioning System (GPS) The Global...Ch. 10.8 - Prob. 48ECh. 10.8 - Prob. 49ECh. 10.9 - To graph an inequality, we first graph the...Ch. 10.9 - Prob. 2ECh. 10.9 - Prob. 3ECh. 10.9 - Prob. 4ECh. 10.9 - Prob. 5ECh. 10.9 - Prob. 6ECh. 10.9 - Prob. 7ECh. 10.9 - Prob. 8ECh. 10.9 - Prob. 9ECh. 10.9 - Prob. 10ECh. 10.9 - Prob. 11ECh. 10.9 - Prob. 12ECh. 10.9 - Prob. 13ECh. 10.9 - Prob. 14ECh. 10.9 - Prob. 15ECh. 10.9 - Prob. 16ECh. 10.9 - Prob. 17ECh. 10.9 - Prob. 18ECh. 10.9 - Prob. 19ECh. 10.9 - Prob. 20ECh. 10.9 - Prob. 21ECh. 10.9 - Prob. 22ECh. 10.9 - Prob. 23ECh. 10.9 - Prob. 24ECh. 10.9 - Prob. 25ECh. 10.9 - Prob. 26ECh. 10.9 - Prob. 27ECh. 10.9 - Prob. 28ECh. 10.9 - Prob. 29ECh. 10.9 - Prob. 30ECh. 10.9 - Prob. 31ECh. 10.9 - Prob. 32ECh. 10.9 - Prob. 33ECh. 10.9 - Prob. 34ECh. 10.9 - Prob. 35ECh. 10.9 - Prob. 36ECh. 10.9 - Prob. 37ECh. 10.9 - Prob. 38ECh. 10.9 - Prob. 39ECh. 10.9 - Prob. 40ECh. 10.9 - Prob. 41ECh. 10.9 - Prob. 42ECh. 10.9 - Prob. 43ECh. 10.9 - Prob. 44ECh. 10.9 - Prob. 45ECh. 10.9 - Prob. 46ECh. 10.9 - Prob. 47ECh. 10.9 - Prob. 48ECh. 10.9 - Prob. 49ECh. 10.9 - Prob. 50ECh. 10.9 - Prob. 51ECh. 10.9 - Prob. 52ECh. 10.9 - Coffee Blends A coffee merchant sells two...Ch. 10.9 - Nutrition A cat food manufacturer uses fish and...Ch. 10.9 - Prob. 55ECh. 10 - Prob. 1RCCCh. 10 - Prob. 2RCCCh. 10 - Prob. 3RCCCh. 10 - Prob. 4RCCCh. 10 - Prob. 5RCCCh. 10 - Prob. 6RCCCh. 10 - Prob. 7RCCCh. 10 - Prob. 8RCCCh. 10 - Prob. 9RCCCh. 10 - 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Anne...Ch. 10 - Prob. 9TCh. 10 - Prob. 10TCh. 10 - Only one of the following matrices has an inverse....Ch. 10 - Prob. 12TCh. 10 - Prob. 13TCh. 10 - Prob. 14TCh. 10 - Find the maximum and minimum values of the given...Ch. 10 - Prob. 2PCh. 10 - Prob. 3PCh. 10 - Find the maximum and minimum value of the given...Ch. 10 - Making Furniture A furniture manufacturer makes...Ch. 10 - A Housing Development A housing contractor has...Ch. 10 - Hauling Fruit A trucker hauls citrus fruit from...Ch. 10 - Manufacturing Calculators A manufacturer of...Ch. 10 - Shipping Televisions An electronics discount chain...Ch. 10 - Prob. 10PCh. 10 - Packaging Nuts A confectioner sells two types of...Ch. 10 - Feeding Lab Rabbits A biologist wishes to feed...Ch. 10 - Investing in Bonds A woman wishes to invest 12,000...Ch. 10 - Prob. 14PCh. 10 - Business Strategy A small software company...Ch. 10 - Feasible Region All parts of this problem refer to...
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