Beginning and Intermediate Algebra
5th Edition
ISBN: 9781259616754
Author: Julie Miller, Molly O'Neill, Nancy Hyde
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 4.3, Problem 11PRE
For Exercises 11–30, solve each system using the method of your choice. For systems that do not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent.
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Question 1. Solve the system
-
x1 x2 + 3x3 + 2x4
-x1 + x22x3 + x4
2x12x2+7x3+7x4
Question 2. Consider the system
= 1
=-2
= 1
3x1 - x2 + ax3
= 1
x1 + 3x2 + 2x3
x12x2+2x3
= -b
= 4
1 For what values of a, b will the system be inconsistent?
2 For what values of a, b will the system have only one solution?
For what values of a, b will the saystem have infinitely many solutions?
Chapter 4 Solutions
Beginning and Intermediate Algebra
Ch. 4.1 - Determine whether the ordered paired is a solution...Ch. 4.1 - Determine whether the ordered paired is a solution...Ch. 4.1 - Solve the system by the graphing method. y = − 3 x...Ch. 4.1 - Solve the system by the graphing method. y = 2 x −...Ch. 4.1 - Solve the system by the graphing.
5.
Ch. 4.1 - Solve the system by the graphing.
6.
Ch. 4.1 - a. A______ of linear equations consists of two or...Ch. 4.1 - For Exercises 2-10, determine if the given point...Ch. 4.1 - Prob. 3PECh. 4.1 - Prob. 4PE
Ch. 4.1 - For Exercises 2-10, determine if the given point...Ch. 4.1 - Prob. 6PECh. 4.1 - Prob. 7PECh. 4.1 - Prob. 8PECh. 4.1 - Prob. 9PECh. 4.1 - Prob. 10PECh. 4.1 - For Exercises 11-14, match the graph of the system...Ch. 4.1 - Prob. 12PECh. 4.1 - Prob. 13PECh. 4.1 - For Exercises 11-14, match the graph of the system...Ch. 4.1 - Prob. 15PECh. 4.1 - Prob. 16PECh. 4.1 - Prob. 17PECh. 4.1 - Prob. 18PECh. 4.1 - Prob. 19PECh. 4.1 - Prob. 20PECh. 4.1 - For Exercises 16-26, determine which system of...Ch. 4.1 - Prob. 22PECh. 4.1 - Prob. 23PECh. 4.1 - Prob. 24PECh. 4.1 - Prob. 25PECh. 4.1 - Prob. 26PECh. 4.1 - Prob. 27PECh. 4.1 - Prob. 28PECh. 4.1 - For Exercises 27-50, solve the system by graphing....Ch. 4.1 - Prob. 30PECh. 4.1 - Prob. 31PECh. 4.1 - Prob. 32PECh. 4.1 - Prob. 33PECh. 4.1 - Prob. 34PECh. 4.1 - Prob. 35PECh. 4.1 - Prob. 36PECh. 4.1 - Prob. 37PECh. 4.1 - Prob. 38PECh. 4.1 - Prob. 39PECh. 4.1 - Prob. 40PECh. 4.1 - Prob. 41PECh. 4.1 - Prob. 42PECh. 4.1 - Prob. 43PECh. 4.1 - Prob. 44PECh. 4.1 - Prob. 45PECh. 4.1 - Prob. 46PECh. 4.1 - Prob. 47PECh. 4.1 - Prob. 48PECh. 4.1 - Prob. 49PECh. 4.1 - Prob. 50PECh. 4.1 - Prob. 51PECh. 4.1 - The cost to rent a 10 ft by 10 ft storage space is...Ch. 4.1 - For the systems graphed in Exercises 53-54,...Ch. 4.1 - For the systems graphed in Exercises 53-54,...Ch. 4.1 - Prob. 55PECh. 4.1 - Prob. 56PECh. 4.1 - One equation in a system of linear equations is x...Ch. 4.1 - Prob. 58PECh. 4.2 - Solve the system by using the substitution method....Ch. 4.2 - Prob. 2SPCh. 4.2 - Prob. 3SPCh. 4.2 - Prob. 4SPCh. 4.2 - Prob. 5SPCh. 4.2 - One number is 16 more than another. Their sum is...Ch. 4.2 - Prob. 7SPCh. 4.2 - For Exercises 1-6, write each pair of lines in...Ch. 4.2 - Prob. 2PECh. 4.2 - Prob. 3PECh. 4.2 - Prob. 4PECh. 4.2 - For Exercises 1-6, write each pair of lines in...Ch. 4.2 - Prob. 6PECh. 4.2 - Prob. 7PECh. 4.2 - Prob. 8PECh. 4.2 - Prob. 9PECh. 4.2 - Prob. 10PECh. 4.2 - Given the system: 4 x − 2 y = − 6 3 x + y...Ch. 4.2 - Prob. 12PECh. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - Prob. 14PECh. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - Prob. 16PECh. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - Prob. 18PECh. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - Prob. 20PECh. 4.2 - Prob. 21PECh. 4.2 - Prob. 22PECh. 4.2 - Prob. 23PECh. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - Prob. 25PECh. 4.2 - Prob. 26PECh. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - Prob. 28PECh. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - Prob. 31PECh. 4.2 - Prob. 32PECh. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - Prob. 35PECh. 4.2 - Prob. 36PECh. 4.2 - Prob. 37PECh. 4.2 - Prob. 38PECh. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - Prob. 42PECh. 4.2 - Prob. 43PECh. 4.2 - Prob. 44PECh. 4.2 - Prob. 45PECh. 4.2 - Prob. 46PECh. 4.2 - Prob. 47PECh. 4.2 - For Exercises 13-48, solve the system by using the...Ch. 4.2 - Prob. 49PECh. 4.2 - For Exercises 49-58, set up a system of linear...Ch. 4.2 - For Exercises 49-58, set up a system of linear...Ch. 4.2 - For Exercises 49-58, set up a system of linear...Ch. 4.2 - For Exercises 49-58, set up a system of linear...Ch. 4.2 - For Exercises 49-58, set up a system of linear...Ch. 4.2 - For Exercises 49-58, set up a system of linear...Ch. 4.2 - For Exercises 49-58, set up a system of linear...Ch. 4.2 - Prob. 57PECh. 4.2 - Prob. 58PECh. 4.2 - Prob. 59PECh. 4.2 - Prob. 60PECh. 4.3 - Solve the system by using the addition method. x +...Ch. 4.3 - Solve the system by using the addition method. 4 x...Ch. 4.3 - Prob. 3SPCh. 4.3 - Solve the system by using the addition method. 15...Ch. 4.3 - Solve the system by using the addition method. 2 3...Ch. 4.3 - Solve the system by using the addition method. 3 x...Ch. 4.3 - For Exercises 1-5, check whether the given ordered...Ch. 4.3 - For Exercises 1-5, check whether the given ordered...Ch. 4.3 - For Exercises 1-5, check whether the given ordered...Ch. 4.3 - For Exercises 1-5, check whether the given ordered...Ch. 4.3 - For Exercises 1-5, check whether the given ordered...Ch. 4.3 - For Exercises 6-7, answer as true or false. Given...Ch. 4.3 - Prob. 7PECh. 4.3 - Given the system 3 x − 4 y = 2 17 x + y = 35 a....Ch. 4.3 - 9. Given the system
a. Which variable, x or y, is...Ch. 4.3 - For Exercises 10-24, solve each system using the...Ch. 4.3 - For Exercises 10-24, solve each system using the...Ch. 4.3 - For Exercises 10-24, solve each system using the...Ch. 4.3 - For Exercises 10-24, solve each system using the...Ch. 4.3 - For Exercises 10-24, solve each system using the...Ch. 4.3 - For Exercises 10-24, solve each system using the...Ch. 4.3 - For Exercises 10-24, solve each system using the...Ch. 4.3 - For Exercises 10-24, solve each system using the...Ch. 4.3 - For Exercises 10-24, solve each system using the...Ch. 4.3 - For Exercises 10-24, solve each system using the...Ch. 4.3 - For Exercises 10-24, solve each system using the...Ch. 4.3 - For Exercises 10-24, solve each system using the...Ch. 4.3 - Prob. 22PECh. 4.3 - Prob. 23PECh. 4.3 - For Exercises 10-24, solve each system using the...Ch. 4.3 - Prob. 25PECh. 4.3 - Prob. 26PECh. 4.3 - Prob. 27PECh. 4.3 - Prob. 28PECh. 4.3 - Prob. 29PECh. 4.3 - 30. Suppose in solving a system of linear...Ch. 4.3 - For Exercises 31-42, solve the system by using the...Ch. 4.3 - Prob. 32PECh. 4.3 - Prob. 33PECh. 4.3 - Prob. 34PECh. 4.3 - Prob. 35PECh. 4.3 - Prob. 36PECh. 4.3 - Prob. 37PECh. 4.3 - Prob. 38PECh. 4.3 - Prob. 39PECh. 4.3 - Prob. 40PECh. 4.3 - Prob. 41PECh. 4.3 - Prob. 42PECh. 4.3 - Prob. 43PECh. 4.3 - Prob. 44PECh. 4.3 - Prob. 45PECh. 4.3 - Prob. 46PECh. 4.3 - Prob. 47PECh. 4.3 - Prob. 48PECh. 4.3 - Prob. 49PECh. 4.3 - Prob. 50PECh. 4.3 - Prob. 51PECh. 4.3 - Prob. 52PECh. 4.3 - Prob. 53PECh. 4.3 - Prob. 54PECh. 4.3 - Prob. 55PECh. 4.3 - Prob. 56PECh. 4.3 - For Exercises 43-63, solve each system of...Ch. 4.3 - Prob. 58PECh. 4.3 - Prob. 59PECh. 4.3 - Prob. 60PECh. 4.3 - Prob. 61PECh. 4.3 - Prob. 62PECh. 4.3 - Prob. 63PECh. 4.3 - Prob. 64PECh. 4.3 - Prob. 65PECh. 4.3 - Prob. 66PECh. 4.3 - Prob. 67PECh. 4.3 - Prob. 68PECh. 4.3 - Prob. 69PECh. 4.3 - For Exercises 70-72, solve the system by using...Ch. 4.3 - For Exercises 70-72, solve the system by using...Ch. 4.3 - For Exercises 70-72, solve the system by using...Ch. 4.3 - 73. Explain why a system of linear equations...Ch. 4.3 - Prob. 74PECh. 4.3 - Prob. 75PECh. 4.3 - For Exercises 1–6 determine the number of...Ch. 4.3 - For Exercises 1–6 determine the number of...Ch. 4.3 - Prob. 3PRECh. 4.3 - Prob. 4PRECh. 4.3 - Prob. 5PRECh. 4.3 - For Exercises 1–6 determine the number of...Ch. 4.3 - For Exercises 7–10, a method of solving has been...Ch. 4.3 - For Exercises 7–10, a method of solving has been...Ch. 4.3 - Prob. 9PRECh. 4.3 - Prob. 10PRECh. 4.3 - For Exercises 11–30, solve each system using the...Ch. 4.3 - For Exercises 11–30, solve each system using the...Ch. 4.3 - Prob. 13PRECh. 4.3 - For Exercises 11–30, solve each system using the...Ch. 4.3 - For Exercises 11–30, solve each system using the...Ch. 4.3 - For Exercises 11–30, solve each system using the...Ch. 4.3 - For Exercises 11–30, solve each system using the...Ch. 4.3 - For Exercises 11–30, solve each system using the...Ch. 4.3 - For Exercises 11–30, solve each system using the...Ch. 4.3 - For Exercises 11–30, solve each system using the...Ch. 4.3 - For Exercises 11–30, solve each system using the...Ch. 4.3 - For Exercises 11–30, solve each system using the...Ch. 4.3 - Prob. 23PRECh. 4.3 - Prob. 24PRECh. 4.3 - Prob. 25PRECh. 4.3 - Prob. 26PRECh. 4.3 - Prob. 27PRECh. 4.3 - Prob. 28PRECh. 4.3 - Prob. 29PRECh. 4.3 - Prob. 30PRECh. 4.4 - 1. Lynn went to a fast-food restaurant and spent...Ch. 4.4 - Prob. 2SPCh. 4.4 - Prob. 3SPCh. 4.4 - Prob. 4SPCh. 4.4 - For Exercises 1-4, solve each system of equations...Ch. 4.4 - Prob. 2PECh. 4.4 - Prob. 3PECh. 4.4 - Prob. 4PECh. 4.4 - Prob. 5PECh. 4.4 - Foe Exercises 5-8, set up a system of linear...Ch. 4.4 - Prob. 7PECh. 4.4 - Prob. 8PECh. 4.4 - 9. An online store sells old video games and DVDs...Ch. 4.4 - Tanya bought three adult tickets and one...Ch. 4.4 - 11. Nora bought 100 shares of a technology stock...Ch. 4.4 - 12. Eight students in Ms. Reese’s class decided to...Ch. 4.4 - 13. Mylee is a stamp collector and buys...Ch. 4.4 - Zoey purchased some beef and some chicken for a...Ch. 4.4 - 15. Shanelle invested $10,000, and at the end of 1...Ch. 4.4 - Prob. 16PECh. 4.4 - Prob. 17PECh. 4.4 - 18. Blake has a total of $4000 to invest in two...Ch. 4.4 - Prob. 19PECh. 4.4 - Prob. 20PECh. 4.4 - How much 50% disinfectant solution must be mixed...Ch. 4.4 - Prob. 22PECh. 4.4 - 23. How much 45% disinfectant solution must be...Ch. 4.4 - Prob. 24PECh. 4.4 - Prob. 25PECh. 4.4 - Prob. 26PECh. 4.4 - Prob. 27PECh. 4.4 - Silvia wants to mix a 40% apple juice drink with...Ch. 4.4 - Prob. 29PECh. 4.4 - Prob. 30PECh. 4.4 - Prob. 31PECh. 4.4 - A plane flies 720 mi with the wind in 3 hr. The...Ch. 4.4 - Prob. 33PECh. 4.4 - Prob. 34PECh. 4.4 - Debi has $2.80 in a collection of dimes and...Ch. 4.4 - Prob. 36PECh. 4.4 - Prob. 37PECh. 4.4 - Prob. 38PECh. 4.4 - In the 1961–1962 NBA basketball season, Wilt...Ch. 4.4 - 40. In the 1971–1972 NBA basketball season, Kareem...Ch. 4.4 - Prob. 41PECh. 4.4 - Prob. 42PECh. 4.4 - A total of $60,000 is invested in two accounts,...Ch. 4.4 - Prob. 44PECh. 4.4 - Prob. 45PECh. 4.4 - Prob. 46PECh. 4.4 - Prob. 47PECh. 4.4 - Prob. 48PECh. 4.4 - Prob. 49PECh. 4.4 - Prob. 50PECh. 4.5 - Solve the system. x + 2 y + z = 1 3 x − y + 2 z =...Ch. 4.5 - Prob. 2SPCh. 4.5 - Prob. 3SPCh. 4.5 - Prob. 4SPCh. 4.5 - Prob. 1PECh. 4.5 - For Exercises 2–4, solve the systems by using two...Ch. 4.5 - Prob. 3PECh. 4.5 - For Exercises 2–4, solve the systems by using two...Ch. 4.5 - Two cars leave Kansas City at the same time. One...Ch. 4.5 - Prob. 6PECh. 4.5 - Which of the following points are solutions to the...Ch. 4.5 - Prob. 8PECh. 4.5 - Prob. 9PECh. 4.5 - Prob. 10PECh. 4.5 - For Exercises 11–34, solve the system of...Ch. 4.5 - For Exercises 11–34, solve the system of...Ch. 4.5 - Prob. 13PECh. 4.5 - Prob. 14PECh. 4.5 - Prob. 15PECh. 4.5 - For Exercises 11–34, solve the system of...Ch. 4.5 - Prob. 17PECh. 4.5 - Prob. 18PECh. 4.5 - Prob. 19PECh. 4.5 - Prob. 20PECh. 4.5 - Prob. 21PECh. 4.5 - Prob. 22PECh. 4.5 - Prob. 23PECh. 4.5 - Prob. 24PECh. 4.5 - Prob. 25PECh. 4.5 - For Exercises 11–34, solve the system of...Ch. 4.5 - For Exercises 11–34, solve the system of...Ch. 4.5 - For Exercises 11–34, solve the system of...Ch. 4.5 - For Exercises 11–34, solve the system of...Ch. 4.5 - For Exercises 11–34, solve the system of...Ch. 4.5 - Prob. 31PECh. 4.5 - Prob. 32PECh. 4.5 - For Exercises 11–34, solve the system of...Ch. 4.5 - Prob. 34PECh. 4.5 - Prob. 35PECh. 4.5 - Prob. 36PECh. 4.5 - Prob. 37PECh. 4.5 - Prob. 38PECh. 4.5 - Prob. 39PECh. 4.5 - Prob. 40PECh. 4.5 - Prob. 41PECh. 4.5 - Prob. 42PECh. 4.5 - For Exercises 35–46, solve the system. If there is...Ch. 4.5 - Prob. 44PECh. 4.5 - Prob. 45PECh. 4.5 - Prob. 46PECh. 4.5 - Prob. 47PECh. 4.5 - Prob. 48PECh. 4.5 - Prob. 49PECh. 4.5 - Prob. 50PECh. 4.6 - 1. The perimeter of a triangle is 30 in. The...Ch. 4.6 - Annette, Barb, and Carlita work in a clothing...Ch. 4.6 - For Exercises 1–4, solve the system. If there is...Ch. 4.6 - Prob. 2PECh. 4.6 - Prob. 3PECh. 4.6 - Prob. 4PECh. 4.6 - Prob. 5PECh. 4.6 - Prob. 6PECh. 4.6 - One angle of a triangle measures 6° more than...Ch. 4.6 - Prob. 8PECh. 4.6 - Prob. 9PECh. 4.6 - 10. The perimeter of a triangle is 5 ft. The...Ch. 4.6 - Prob. 11PECh. 4.6 - Prob. 12PECh. 4.6 - Prob. 13PECh. 4.6 - Prob. 14PECh. 4.6 - Prob. 15PECh. 4.6 - Prob. 16PECh. 4.6 - Prob. 17PECh. 4.6 - Prob. 18PECh. 4.6 - Prob. 19PECh. 4.6 - Prob. 20PECh. 4.6 - Prob. 21PECh. 4.6 - Souvenir hats, T-shirts, and jackets are sold at a...Ch. 4.6 - Prob. 23PECh. 4.6 - Prob. 24PECh. 4 - For Exercises 1–4, determine if the ordered pair...Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - For Exercises 11–18, solve the system by graphing....Ch. 4 - For Exercises 11–18, solve the system by graphing....Ch. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - For Exercises 11–18, solve the system by graphing....Ch. 4 - Prob. 18RECh. 4 - Once phone company charges $0.15 a minute for...Ch. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - 25. Given the system:
a. Which variable from...Ch. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Given the system. 3 x − 5 y = 1 2 x − y = − 4 a....Ch. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - For Exercises 53–58, solve the systems of...Ch. 4 - For Exercises 53–58, solve the systems of...Ch. 4 - For Exercises 53–58, solve the systems of...Ch. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - For Exercises 53–58, solve the systems of...Ch. 4 - Prob. 59RECh. 4 - Prob. 60RECh. 4 - Prob. 61RECh. 4 - 62. In a triangle, the largest angle measures 76°...Ch. 4 - Prob. 1TCh. 4 - Prob. 2TCh. 4 - Prob. 3TCh. 4 - Prob. 4TCh. 4 - Prob. 5TCh. 4 - Prob. 6TCh. 4 - Prob. 7TCh. 4 - 8. a. How many solutions does a system of two...Ch. 4 - Prob. 9TCh. 4 - For Exercises 9–14, solve each system using any...Ch. 4 - For Exercises 9–14, solve each system using any...Ch. 4 - Prob. 12TCh. 4 - Prob. 13TCh. 4 - Prob. 14TCh. 4 - Latrell buys four CDs and two DVDs for $54 from...Ch. 4 - Prob. 16TCh. 4 - Prob. 17TCh. 4 - Prob. 18TCh. 4 - 19. A plane travels 910 mi in 2 hr against the...Ch. 4 - Prob. 20TCh. 4 - Prob. 21TCh. 4 - Prob. 22TCh. 4 - Prob. 23TCh. 4 - Prob. 24TCh. 4 - Prob. 25TCh. 4 - Prob. 26TCh. 4 - Prob. 27TCh. 4 - Prob. 1CRECh. 4 - Prob. 2CRECh. 4 - Prob. 3CRECh. 4 - Prob. 4CRECh. 4 - Prob. 5CRECh. 4 - Prob. 6CRECh. 4 - Prob. 7CRECh. 4 - Prob. 8CRECh. 4 - Prob. 9CRECh. 4 - Prob. 10CRECh. 4 - Prob. 11CRECh. 4 - Prob. 12CRECh. 4 - Prob. 13CRECh. 4 - Prob. 14CRECh. 4 - Sketch the following equations on the same graph....Ch. 4 - Prob. 16CRECh. 4 - Prob. 17CRECh. 4 - Use a system of linear equations to solve for x...Ch. 4 - In 1920, the average speed for the winner of the...Ch. 4 - Prob. 20CRE
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- Question 6 Not yet answered Marked out of 5.00 Flag question = If (4,6,-11) and (-12,-16,4), = Compute the cross product vx w karrow_forwardConsider the following vector field v^-> (x,y): v^->(x,y)=2yi−xj What is the magnitude of the vector v⃗ located in point (13,9)? [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places]arrow_forwardQuestion 4 Find the value of the first element for the first row of the inverse matrix of matrix B. 3 Not yet answered B = Marked out of 5.00 · (³ ;) Flag question 7 [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places] Answer:arrow_forward
- Question 2 Not yet answered Multiply the following Matrices together: [77-4 A = 36 Marked out of -5 -5 5.00 B = 3 5 Flag question -6 -7 ABarrow_forwardAssume {u1, U2, u3, u4} does not span R³. Select the best statement. A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set. B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³. C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set. D. {u1, U2, u3} cannot span R³. E. {U1, U2, u3} spans R³ if u̸4 is the zero vector. F. none of the abovearrow_forwardSelect the best statement. A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors are distinct. n B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0 excluded spans Rª. ○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n vectors. ○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors spans Rn. E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn. F. none of the abovearrow_forward
- Which of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.) ☐ A. { 7 4 3 13 -9 8 -17 7 ☐ B. 0 -8 3 ☐ C. 0 ☐ D. -5 ☐ E. 3 ☐ F. 4 THarrow_forward3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forward(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0arrow_forward
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