Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Chapter 9 Solutions
Algebra and Trigonometry (6th Edition)
Ch. 9.1 - Fill in each blank so that the resulting statement...Ch. 9.1 - Fill in each blank so that the resulting statement...Ch. 9.1 - Prob. 3CVCCh. 9.1 - Prob. 4CVCCh. 9.1 - Fill in each blank so that the resulting statement...Ch. 9.1 - Fill in each blank so that the resulting statement...Ch. 9.1 - In Exercises 1-8, write the augmented matrix for...Ch. 9.1 - In Exercises 1-8, write the augmented matrix for...Ch. 9.1 - In Exercises 18, write the augmented matrix for...Ch. 9.1 - In Exercises 1-8, write the augmented matrix for...
Ch. 9.1 - In Exercises 1-8, write the augmented matrix for...Ch. 9.1 - In Exercises 1-8, write the augmented matrix for...Ch. 9.1 - In Exercises 1-8, write the augmented matrix for...Ch. 9.1 - In Exercises 1-8, write the augmented matrix for...Ch. 9.1 - In Exercises 9-12, write the system of linear...Ch. 9.1 - In Exercises 9-12, write the system of linear...Ch. 9.1 - In Exercises 9-12, write the system of linear...Ch. 9.1 - In Exercises 9-12, write the system of linear...Ch. 9.1 - In Exercises 13-18, perform each matrix row...Ch. 9.1 - In Exercises 13-18, perform each matrix row...Ch. 9.1 - In Exercises 13-18, perform each matrix row...Ch. 9.1 - 16.
Ch. 9.1 - In Exercises 13-18, perform each matrix row...Ch. 9.1 - In Exercises 13-18, perform each matrix row...Ch. 9.1 - In Exercises 19-20, a few steps in the process of...Ch. 9.1 - In Exercises 19-20, a few steps in the process of...Ch. 9.1 - In Exercises 21-38, solve each system of equations...Ch. 9.1 - In Exercises 21-38, solve each system of equations...Ch. 9.1 - In Exercises 21-38, solve each system of equations...Ch. 9.1 - In Exercises 21-38 solve each system of equations...Ch. 9.1 - In Exercises 21-38, solve each system of equations...Ch. 9.1 - In Exercises 21-38, solve each system of equations...Ch. 9.1 - In Exercises 21-38, solve each system of equations...Ch. 9.1 - In Exercises 21-38, solve each system of equations...Ch. 9.1 - In Exercises 21-38, solve each system of equations...Ch. 9.1 - In Exercises 21-38, solve each system of equations...Ch. 9.1 - In Exercises 21-38, solve each system of equations...Ch. 9.1 - In Exercises 21-38, solve each system of equations...Ch. 9.1 - In Exercises 21-38, solve each system of...Ch. 9.1 - { 3x+2y+3z=34x5y+7z=12x+3y2z=6Ch. 9.1 - In Exercises 21-38. solve each system of equal...Ch. 9.1 - In Exercises 21-38, solve each system of equations...Ch. 9.1 - In Exercises 21-38. solve each system of equations...Ch. 9.1 - In Exercises 21-38. solve each system of equations...Ch. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - 41. Find the cubic function
Ch. 9.1 - Find the cubic function...Ch. 9.1 - Prob. 43ECh. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Write a system of linear equations in three or...Ch. 9.1 - What is a matrix?Ch. 9.1 - Prob. 52ECh. 9.1 - In your own words, describe each of the three...Ch. 9.1 - Prob. 54ECh. 9.1 - What is the difference between Gaussian...Ch. 9.1 - Most graphing utilities can perform row operations...Ch. 9.1 - Prob. 57ECh. 9.1 - Prob. 58ECh. 9.1 - Make Sense? In Exercises 59-62, determine whether...Ch. 9.1 - Prob. 60ECh. 9.1 - Prob. 61ECh. 9.1 - Prob. 62ECh. 9.1 - Prob. 63ECh. 9.1 - Prob. 64ECh. 9.1 - Prob. 65ECh. 9.1 - Prob. 66ECh. 9.1 - Prob. 67ECh. 9.1 - Prob. 68ECh. 9.1 - Prob. 69ECh. 9.1 - Prob. 70ECh. 9.1 - Prob. 71ECh. 9.1 - Prob. 72ECh. 9.1 - Prob. 73ECh. 9.1 - Exercises 72-74 will help you prepare for the...Ch. 9.2 - Fill in each blank so that the resulting statement...Ch. 9.2 - Prob. 2CVCCh. 9.2 - Prob. 3CVCCh. 9.2 - True or false: If (2z+3,5z1,z) is the solution set...Ch. 9.2 - Using Gaussian elimination to solve {...Ch. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - In Exercises 1-24, use Gaussian elimination to...Ch. 9.2 - Prob. 7ECh. 9.2 - In Exercises 1-24, use Gaussian elimination to...Ch. 9.2 - In Exercises 1-24, use Gaussian elimination to...Ch. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - In Exercises 1-24, use Gaussian elimination to...Ch. 9.2 - In Exercises 1-24, use Gaussian elimination to...Ch. 9.2 - Practice Exercises In Exercises 1-24, use Gaussian...Ch. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - In Exercises 1-24, use Gaussian elimination to...Ch. 9.2 - In Exercises 1-24, use Gaussian elimination to...Ch. 9.2 - Prob. 19ECh. 9.2 - In Exercises 1-24, use Gaussian elimination to...Ch. 9.2 - In Exercises 1-24, use Gaussian elimination to...Ch. 9.2 - Prob. 22ECh. 9.2 - In Exercises 1-24, use Gaussian elimination to...Ch. 9.2 - In Exercises 1-24, use Gaussian elimination to...Ch. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - The vitamin content per ounce for three foods is...Ch. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Describe what happens when Gaussian elimination is...Ch. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - a The figure shows die intersections of a number...Ch. 9.2 - Make Sense? In Exercises 41—44, determine whether...Ch. 9.2 - Make Sense? In Exercises 41-44, determine whether...Ch. 9.2 - Make Sense? In Exercises 41-44, determine whether...Ch. 9.2 - Prob. 44ECh. 9.2 - Consider the linear system {...Ch. 9.2 - Before beginning this exercise, the group needs to...Ch. 9.2 - You are choosing between two cellphone plans. Data...Ch. 9.2 - Find the inverse of f(x)=3x4.. (Section 2.7....Ch. 9.2 - A chemist needs to mix a 75% saltwater solution...Ch. 9.2 - 50. Solve: cos x tan2 x = 3 cos (Section 6.5....Ch. 9.2 - Exercises 51-53 will help you prepare for the...Ch. 9.2 - Exercises 51-53 will help you prepare for the...Ch. 9.2 - Exercises 51-53 will help you prepare for the...Ch. 9.3 - Fill in each blank so that the resulting statement...Ch. 9.3 - Fill in each blank so that the resulting statement...Ch. 9.3 - Fill in each blank so that the resulting statement...Ch. 9.3 - Fill in each blank so that the resulting statement...Ch. 9.3 - Prob. 5CVCCh. 9.3 - Prob. 6CVCCh. 9.3 - Prob. 7CVCCh. 9.3 - Prob. 8CVCCh. 9.3 - Prob. 9CVCCh. 9.3 - Prob. 10CVCCh. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - In Exercises 5-8, find values for the variables so...Ch. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - In Exercises 17-26, let
and
Solve each matrix...Ch. 9.3 - In Exercises 17-26, let A=[ 372950 ] and B=[...Ch. 9.3 - Prob. 26ECh. 9.3 - Prob. 27ECh. 9.3 - In Exercises 27-36, find (if possible) the...Ch. 9.3 - Prob. 29ECh. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - In Exercises 27-36, find (if possible) the...Ch. 9.3 - Prob. 35ECh. 9.3 - Prob. 36ECh. 9.3 - Prob. 37ECh. 9.3 - Prob. 38ECh. 9.3 - Prob. 39ECh. 9.3 - Prob. 40ECh. 9.3 - Prob. 41ECh. 9.3 - Prob. 42ECh. 9.3 - Prob. 43ECh. 9.3 - Prob. 44ECh. 9.3 - Prob. 45ECh. 9.3 - Prob. 46ECh. 9.3 - Prob. 47ECh. 9.3 - Prob. 48ECh. 9.3 - In Exercises 49-50, suppose that the vertices of a...Ch. 9.3 - Prob. 50ECh. 9.3 - The -5- sign in the figure is shown using 9 pixels...Ch. 9.3 - Prob. 52ECh. 9.3 - Prob. 53ECh. 9.3 - Prob. 54ECh. 9.3 - Prob. 55ECh. 9.3 - Prob. 56ECh. 9.3 - Prob. 57ECh. 9.3 - Prob. 58ECh. 9.3 - Prob. 59ECh. 9.3 - Prob. 60ECh. 9.3 - Prob. 61ECh. 9.3 - 62. The table gives an estimate of basic caloric...Ch. 9.3 - Prob. 63ECh. 9.3 - Prob. 64ECh. 9.3 - Prob. 65ECh. 9.3 - Prob. 66ECh. 9.3 - Prob. 67ECh. 9.3 - How arc matrices added?Ch. 9.3 - Prob. 69ECh. 9.3 - 70. Describe matrices that cannot be added or...Ch. 9.3 - Prob. 71ECh. 9.3 - Prob. 72ECh. 9.3 - Prob. 73ECh. 9.3 - Prob. 74ECh. 9.3 - Prob. 75ECh. 9.3 - Prob. 76ECh. 9.3 - Prob. 77ECh. 9.3 - Prob. 78ECh. 9.3 - Prob. 79ECh. 9.3 - Prob. 80ECh. 9.3 - Prob. 81ECh. 9.3 - Prob. 82ECh. 9.3 - Prob. 83ECh. 9.3 - Prob. 84ECh. 9.3 - Prob. 85ECh. 9.3 - Prob. 86ECh. 9.3 - Prob. 87ECh. 9.3 - 88. Use the Law of Sines to solve the triangle...Ch. 9.3 - Prob. 89ECh. 9.3 - Prob. 90ECh. 9.3 - Exercises 89-91 will help you prepare for the...Ch. 9.4 - Fill in each blank so that the resulting statement...Ch. 9.4 - Prob. 2CVCCh. 9.4 - Prob. 3CVCCh. 9.4 - Prob. 4CVCCh. 9.4 - Fill in each blank so that the resulting statement...Ch. 9.4 - Prob. 6CVCCh. 9.4 - Prob. 7CVCCh. 9.4 - Prob. 8CVCCh. 9.4 - Prob. 9CVCCh. 9.4 - In Exercises 1-12, find the products AB and BA to...Ch. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - In Exercises 1-12, find the products AB and BA to...Ch. 9.4 - Prob. 6ECh. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - In Exercises 1-12, find the products AB and BA to...Ch. 9.4 - Prob. 12ECh. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - Prob. 18ECh. 9.4 - Prob. 19ECh. 9.4 - Prob. 20ECh. 9.4 - Prob. 21ECh. 9.4 - Prob. 22ECh. 9.4 - Prob. 23ECh. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.4 - Prob. 26ECh. 9.4 - Prob. 27ECh. 9.4 - Prob. 28ECh. 9.4 - Prob. 29ECh. 9.4 - Prob. 30ECh. 9.4 - Prob. 31ECh. 9.4 - Prob. 32ECh. 9.4 - Prob. 33ECh. 9.4 - Prob. 34ECh. 9.4 - Prob. 35ECh. 9.4 - Prob. 36ECh. 9.4 - Prob. 37ECh. 9.4 - Prob. 38ECh. 9.4 - Prob. 39ECh. 9.4 - Prob. 40ECh. 9.4 - Prob. 41ECh. 9.4 - Prob. 42ECh. 9.4 - Prob. 43ECh. 9.4 - Prob. 44ECh. 9.4 - Prob. 45ECh. 9.4 - Prob. 46ECh. 9.4 - Prob. 47ECh. 9.4 - Prob. 48ECh. 9.4 - Prob. 49ECh. 9.4 - Prob. 50ECh. 9.4 - Prob. 51ECh. 9.4 - Prob. 52ECh. 9.4 - Prob. 53ECh. 9.4 - Prob. 54ECh. 9.4 - Prob. 55ECh. 9.4 - Prob. 56ECh. 9.4 - Explain why a matrix that does not have the same...Ch. 9.4 - 58. Explain how to find the multiplicative inverse...Ch. 9.4 - Prob. 59ECh. 9.4 - Prob. 60ECh. 9.4 - Prob. 61ECh. 9.4 - Prob. 62ECh. 9.4 - Prob. 63ECh. 9.4 - A year has passed since Exercise 63. (Tune flies...Ch. 9.4 - Prob. 65ECh. 9.4 - Prob. 66ECh. 9.4 - Prob. 67ECh. 9.4 - Prob. 68ECh. 9.4 - Prob. 69ECh. 9.4 - Prob. 70ECh. 9.4 - Prob. 71ECh. 9.4 - Prob. 72ECh. 9.4 - Prob. 73ECh. 9.4 - Prob. 74ECh. 9.4 - Prob. 75ECh. 9.4 - Prob. 76ECh. 9.4 - Prob. 77ECh. 9.4 - Prob. 78ECh. 9.4 - Prob. 79ECh. 9.4 - Prob. 80ECh. 9.4 - Prob. 81ECh. 9.4 - Prob. 82ECh. 9.4 - Prob. 83ECh. 9.4 - Prob. 84ECh. 9.4 - Prob. 85ECh. 9.4 - Prob. 86ECh. 9.4 - Prob. 87ECh. 9.4 - Prob. 88ECh. 9.4 - Give an example of a 22 matrix that is its own...Ch. 9.4 - Prob. 90ECh. 9.4 - Prob. 91ECh. 9.4 - Prob. 92ECh. 9.4 - Prob. 93ECh. 9.4 - Prob. 94ECh. 9.4 - Prob. 95ECh. 9.4 - Prob. 96ECh. 9.4 - Prob. 97ECh. 9.4 - Prob. 98ECh. 9.4 - Prob. 99ECh. 9.5 - 1.
The value of this second-order_________...Ch. 9.5 - Using Cramers Rule to solve { x+y=8xy=2 we obtain...Ch. 9.5 - | 321431511 |=3| |4| |Ch. 9.5 - Prob. 4CVCCh. 9.5 - Prob. 5CVCCh. 9.5 - Evaluate each determinant in Exercises 1-10.
1.
Ch. 9.5 - Evaluate each determinant in Exercises 1-10.
2.
Ch. 9.5 - Evaluate each determinant in Exercises 1-10. |...Ch. 9.5 - Evaluate each determinant in Exercises 1-10.
4.
Ch. 9.5 - Evaluate each determinant in Exercises 1-10. |...Ch. 9.5 - Evaluate each determinant in Exercises 1-10. |...Ch. 9.5 - Evaluate each determinant in Exercises 1-10. |...Ch. 9.5 - Evaluate each determinant in Exercises 1-10. |...Ch. 9.5 - Evaluate each determinant in Exercises 1-10. |...Ch. 9.5 - Evaluate each determinant in Exercises 1-10.
10.
Ch. 9.5 - For Exercises 11-22, use Cramer’s Rule to solve...Ch. 9.5 - Prob. 12ECh. 9.5 - Prob. 13ECh. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Prob. 21ECh. 9.5 - Prob. 22ECh. 9.5 - Prob. 23ECh. 9.5 - Prob. 24ECh. 9.5 - Prob. 25ECh. 9.5 - Prob. 26ECh. 9.5 - Prob. 27ECh. 9.5 - Prob. 28ECh. 9.5 - In Exercises 29-36, use Cramer's Rule to solve...Ch. 9.5 - In Exercises 29-36, use Cramer's Rule to solve...Ch. 9.5 - In Exercises 29-36, use Cramer's Rule to solve...Ch. 9.5 - Prob. 32ECh. 9.5 - Prob. 33ECh. 9.5 - Prob. 34ECh. 9.5 - Prob. 35ECh. 9.5 - Prob. 36ECh. 9.5 - Evaluate each determinant in Exercises 37-40....Ch. 9.5 - Prob. 38ECh. 9.5 - Evaluate each determinant in Exercises 37-40. |...Ch. 9.5 - Prob. 40ECh. 9.5 - Prob. 41ECh. 9.5 - Prob. 42ECh. 9.5 - Prob. 43ECh. 9.5 - Prob. 44ECh. 9.5 - Prob. 45ECh. 9.5 - Prob. 46ECh. 9.5 - Prob. 47ECh. 9.5 - Prob. 48ECh. 9.5 - Prob. 49ECh. 9.5 - Prob. 50ECh. 9.5 - Prob. 51ECh. 9.5 - Prob. 52ECh. 9.5 - Prob. 53ECh. 9.5 - Prob. 54ECh. 9.5 - Prob. 55ECh. 9.5 - Prob. 56ECh. 9.5 - Prob. 57ECh. 9.5 - Prob. 58ECh. 9.5 - Prob. 59ECh. 9.5 - Prob. 60ECh. 9.5 - Prob. 61ECh. 9.5 - Prob. 62ECh. 9.5 - Prob. 63ECh. 9.5 - Prob. 64ECh. 9.5 - Prob. 65ECh. 9.5 - Prob. 66ECh. 9.5 - Prob. 67ECh. 9.5 - Prob. 68ECh. 9.5 - Prob. 69ECh. 9.5 - Prob. 70ECh. 9.5 - Prob. 71ECh. 9.5 - Prob. 72ECh. 9.5 - Prob. 73ECh. 9.5 - Prob. 74ECh. 9.5 - Prob. 75ECh. 9.5 - Prob. 76ECh. 9.5 - Prob. 77ECh. 9.5 - Prob. 78ECh. 9.5 - Prob. 79ECh. 9.5 - Prob. 80ECh. 9.5 - Prob. 81ECh. 9.5 - Prob. 82ECh. 9.5 - Prob. 83ECh. 9 - In Exercises 1-5, use matrices to find the...Ch. 9 - In Exercises 1-5. use matrices to find the...Ch. 9 - Prob. 3MCCPCh. 9 - Prob. 4MCCPCh. 9 - Prob. 5MCCPCh. 9 - Prob. 6MCCPCh. 9 - Prob. 7MCCPCh. 9 - Prob. 8MCCPCh. 9 - Prob. 9MCCPCh. 9 - Prob. 10MCCPCh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - The figure shows a right triangle in a rectangular...Ch. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - In Exercises 52-55, use Cramers’s Rule to solve...Ch. 9 - Prob. 1TCh. 9 - Prob. 2TCh. 9 - Prob. 3TCh. 9 - Prob. 4TCh. 9 - Prob. 5TCh. 9 - Prob. 6TCh. 9 - Prob. 7TCh. 9 - Prob. 8TCh. 9 - Prob. 9TCh. 9 - Prob. 10TCh. 9 - Prob. 1CRECh. 9 - Prob. 2CRECh. 9 - Prob. 3CRECh. 9 - Prob. 4CRECh. 9 - Prob. 5CRECh. 9 - Prob. 6CRECh. 9 - Prob. 7CRECh. 9 - Prob. 8CRECh. 9 - Prob. 9CRECh. 9 - Prob. 10CRECh. 9 - Prob. 11CRECh. 9 - Prob. 12CRECh. 9 - Prob. 13CRECh. 9 - Prob. 14CRECh. 9 - Prob. 15CRECh. 9 - Prob. 16CRECh. 9 - Prob. 17CRECh. 9 - Prob. 18CRECh. 9 - Prob. 19CRECh. 9 - Prob. 20CRECh. 9 - Prob. 21CRECh. 9 - Prob. 22CRECh. 9 - Prob. 23CRECh. 9 - Prob. 24CRECh. 9 - Prob. 25CRE
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- Select 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_forwardWhich 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_forwardFind the perimeter and areaarrow_forwardAssume {u1, U2, us} spans R³. Select the best statement. A. {U1, U2, us, u4} spans R³ unless u is the zero vector. B. {U1, U2, us, u4} always spans R³. C. {U1, U2, us, u4} spans R³ unless u is a scalar multiple of another vector in the set. D. We do not have sufficient information to determine if {u₁, u2, 43, 114} spans R³. OE. {U1, U2, 3, 4} never spans R³. F. none of the abovearrow_forward
- Assume {u1, U2, 13, 14} spans R³. Select the best statement. A. {U1, U2, u3} never spans R³ since it is a proper subset of a spanning set. B. {U1, U2, u3} spans R³ unless one of the vectors is the zero vector. C. {u1, U2, us} spans R³ unless one of the vectors is a scalar multiple of another vector in the set. D. {U1, U2, us} always spans R³. E. {U1, U2, u3} may, but does not have to, span R³. F. none of the abovearrow_forwardLet H = span {u, v}. For each of the following sets of vectors determine whether H is a line or a plane. Select an Answer u = 3 1. -10 8-8 -2 ,v= 5 Select an Answer -2 u = 3 4 2. + 9 ,v= 6arrow_forwardSolve for the matrix X: X (2 7³) x + ( 2 ) - (112) 6 14 8arrow_forward
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