Beginning and Intermediate Algebra (6th Edition)
6th Edition
ISBN: 9780321969163
Author: Margaret L. Lial, John Hornsby, Terry McGinnis
Publisher: PEARSON
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Chapter R.2, Problem 15E
To determine
To calculate: The value of
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Assume {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 above
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 above
Assume {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 above
Chapter R Solutions
Beginning and Intermediate Algebra (6th Edition)
Ch. R.1 - Concept Check Decide whether each statement is...Ch. R.1 - Concept Check Decide whether each statement is...Ch. R.1 - Concept Check Decide whether each statement is...Ch. R.1 - Concept Check Decide whether each statement is...Ch. R.1 - Concept Check Decide whether each statement is...Ch. R.1 - Prob. 6ECh. R.1 - Concept Check Decide whether each statement is...Ch. R.1 - Concept Check Decide whether each statement is...Ch. R.1 - Prob. 9ECh. R.1 - Concept Check Choose the letter of the correct...
Ch. R.1 - Prob. 11ECh. R.1 - Prob. 12ECh. R.1 - Identify each number as prime, composite, or...Ch. R.1 - Prob. 14ECh. R.1 - Prob. 15ECh. R.1 - Prob. 16ECh. R.1 - Prob. 17ECh. R.1 - Prob. 18ECh. R.1 - Prob. 19ECh. R.1 - Prob. 20ECh. R.1 - Identify each number as prime, composite, or...Ch. R.1 - Prob. 22ECh. R.1 - Prob. 23ECh. R.1 - Prob. 24ECh. R.1 - Prob. 25ECh. R.1 - Identify each number as prime, composite, or...Ch. R.1 - Identify each number as prime, composite, or...Ch. R.1 - Identify each number as prime, composite, or...Ch. R.1 - Prob. 29ECh. R.1 - Prob. 30ECh. R.1 - Write each fraction in lowest terms. See Example...Ch. R.1 - Write each fraction in lowest terms. See Example...Ch. R.1 - Write each fraction in lowest terms. See Example...Ch. R.1 - Write each fraction in lowest terms. See Example...Ch. R.1 - Write each fraction in lowest terms. See Example...Ch. R.1 - Write each fraction in lowest terms. See Example...Ch. R.1 - Write each fraction in lowest terms. See Example...Ch. R.1 - Prob. 38ECh. R.1 - Write each fraction in lowest terms. See Example...Ch. R.1 - Write each fraction in lowest terms. See Example...Ch. R.1 - Prob. 41ECh. R.1 - Prob. 42ECh. R.1 - Prob. 43ECh. R.1 - Prob. 44ECh. R.1 - Prob. 45ECh. R.1 - Prob. 46ECh. R.1 - Prob. 47ECh. R.1 - Prob. 48ECh. R.1 - Write each mixed number as an improper fraction....Ch. R.1 - Prob. 50ECh. R.1 - Prob. 51ECh. R.1 - Prob. 52ECh. R.1 - Prob. 53ECh. R.1 - Prob. 54ECh. R.1 - Prob. 55ECh. R.1 - Prob. 56ECh. R.1 - Prob. 57ECh. R.1 - Prob. 58ECh. R.1 - Prob. 59ECh. R.1 - Prob. 60ECh. R.1 - Prob. 61ECh. R.1 - Prob. 62ECh. R.1 - Prob. 63ECh. R.1 - Prob. 64ECh. R.1 - Prob. 65ECh. R.1 - Prob. 66ECh. R.1 - Prob. 67ECh. R.1 - Prob. 68ECh. R.1 - Prob. 69ECh. R.1 - Prob. 70ECh. R.1 - Prob. 71ECh. R.1 - Prob. 72ECh. R.1 - Prob. 73ECh. R.1 - Prob. 74ECh. R.1 - Prob. 75ECh. R.1 - Prob. 76ECh. R.1 - Find each product or quotient, and write it in...Ch. R.1 - Prob. 78ECh. R.1 - Prob. 79ECh. R.1 - Prob. 80ECh. R.1 - Find each sum or difference, and write it in...Ch. R.1 - Prob. 82ECh. R.1 - Find each sum or difference, and write it in...Ch. R.1 - Prob. 84ECh. R.1 - Prob. 85ECh. R.1 - Prob. 86ECh. R.1 - Prob. 87ECh. R.1 - Prob. 88ECh. R.1 - Prob. 89ECh. R.1 - Prob. 90ECh. R.1 - Prob. 91ECh. R.1 - Prob. 92ECh. R.1 - Prob. 93ECh. R.1 - Prob. 94ECh. R.1 - Prob. 95ECh. R.1 - Prob. 96ECh. R.1 - Prob. 97ECh. R.1 - Prob. 98ECh. R.1 - Prob. 99ECh. R.1 - Prob. 100ECh. R.1 - Prob. 101ECh. R.1 - Prob. 102ECh. R.1 - Prob. 103ECh. R.1 - Prob. 104ECh. R.1 - Work each problem involving fractions. For each...Ch. R.1 - Prob. 106ECh. R.1 - Prob. 107ECh. R.1 - Prob. 108ECh. R.1 - Prob. 109ECh. R.1 - Prob. 110ECh. R.1 - Prob. 111ECh. R.1 - Prob. 112ECh. R.1 - Prob. 113ECh. R.1 - Prob. 114ECh. R.1 - Prob. 115ECh. R.1 - Prob. 116ECh. R.1 - Prob. 117ECh. R.1 - Prob. 118ECh. R.1 - Prob. 119ECh. R.1 - Prob. 120ECh. R.1 - Prob. 121ECh. R.1 - Prob. 122ECh. R.1 - Approximately 40 million people living in the...Ch. R.1 - Prob. 124ECh. R.1 - Prob. 125ECh. R.1 - Approximately 40 million people living in the...Ch. R.1 - Extending Skills Choose the letter of the correct...Ch. R.1 - Prob. 128ECh. R.2 - Concept Check In Exercises 1–4, provide the...Ch. R.2 - Concept Check In Exercises 14, provide the correct...Ch. R.2 - Prob. 3ECh. R.2 - Prob. 4ECh. R.2 - Prob. 5ECh. R.2 - Write each decimal as a fraction. (Do not write in...Ch. R.2 - Prob. 7ECh. R.2 - Write each decimal as a fraction. (Do not write in...Ch. R.2 - Prob. 9ECh. R.2 - Write each decimal as a fraction. (Do not write in...Ch. R.2 - Prob. 11ECh. R.2 - Write each decimal as a fraction. (Do not write in...Ch. R.2 - Prob. 13ECh. R.2 - Write each decimal as a fraction. (Do not write in...Ch. R.2 - Prob. 15ECh. R.2 - Add or subtract as indicated. See Example...Ch. R.2 - Prob. 17ECh. R.2 - Prob. 18ECh. R.2 - Add or subtract as indicated. See Example 2....Ch. R.2 - Prob. 20ECh. R.2 - Add or subtract as indicated. See Example...Ch. R.2 - Prob. 22ECh. R.2 - Add or subtract as indicated. See Example 2....Ch. R.2 - Add or subtract as indicated. See Example 2....Ch. R.2 - Prob. 25ECh. R.2 - Add or subtract as indicated. See Example 2.
26.
Ch. R.2 - Prob. 27ECh. R.2 - Multiply or divide as indicated. See Examples 35....Ch. R.2 - Prob. 29ECh. R.2 - Prob. 30ECh. R.2 - Multiply or divide as indicated. See Examples 35....Ch. R.2 - Prob. 32ECh. R.2 - Multiply or divide as indicated. See Examples...Ch. R.2 - Prob. 34ECh. R.2 - Prob. 35ECh. R.2 - Multiply or divide as indicated. See Examples 35....Ch. R.2 - Prob. 37ECh. R.2 - Multiply or divide as indicated. See Examples...Ch. R.2 - Prob. 39ECh. R.2 - Prob. 40ECh. R.2 - Multiply or divide as indicated. See Examples...Ch. R.2 - Prob. 42ECh. R.2 - Concept Check Complete the following table of...Ch. R.2 - Prob. 44ECh. R.2 - Concept Check Complete the following table of...Ch. R.2 - Prob. 46ECh. R.2 - Concept Check Complete the following table of...Ch. R.2 - Prob. 48ECh. R.2 - Concept Check Complete the following table of...Ch. R.2 - Prob. 50ECh. R.2 - Concept Check Complete the following table of...Ch. R.2 - Prob. 52ECh. R.2 - Prob. 53ECh. R.2 - Concept Check Complete the following table of...Ch. R.2 - Write each fraction as a decimal. For repeating...Ch. R.2 - Prob. 56ECh. R.2 - Write each fraction as a decimal. For repeating...Ch. R.2 - Prob. 58ECh. R.2 - Write each fraction as a decimal. For repeating...Ch. R.2 - Prob. 60ECh. R.2 - Prob. 61ECh. R.2 - Prob. 62ECh. R.2 - Write each percent as a decimal. See Examples 7...Ch. R.2 - Prob. 64ECh. R.2 - Write each percent as a decimal. See Examples 7...Ch. R.2 - Prob. 66ECh. R.2 - Write each percent as a decimal. See Examples 7...Ch. R.2 - Prob. 68ECh. R.2 - Write each percent as a decimal. See Examples 7...Ch. R.2 - Prob. 70ECh. R.2 - Write each percent as a decimal. See Examples 7...Ch. R.2 - Prob. 72ECh. R.2 - Write each percent as a decimal. See Examples 7...Ch. R.2 - Write each percent as a decimal. See Examples 7...Ch. R.2 - Prob. 75ECh. R.2 - Prob. 76ECh. R.2 - Write each decimal as a percent. See Examples 8...Ch. R.2 - Write each decimal as a percent. See Examples 8...Ch. R.2 - Prob. 79ECh. R.2 - Write each decimal as a percent. See Examples 8...Ch. R.2 - Prob. 81ECh. R.2 - Write each decimal as a percent. See Examples 8...Ch. R.2 - Prob. 83ECh. R.2 - Prob. 84ECh. R.2 - Write each decimal as a percent. See Examples 8...Ch. R.2 - Write each decimal as a percent. See Examples 8...Ch. R.2 - Prob. 87ECh. R.2 - Prob. 88ECh. R.2 - Prob. 89ECh. R.2 - Write each percent as a fraction. Give answers in...Ch. R.2 - Prob. 91ECh. R.2 - Write each percent as a fraction. Give answers in...Ch. R.2 - Prob. 93ECh. R.2 - Write each percent as a fraction. Give answers in...Ch. R.2 - Write each percent as a fraction. Give answers in...Ch. R.2 - Prob. 96ECh. R.2 - Prob. 97ECh. R.2 - Write each fraction as a percent. See Example...Ch. R.2 - Prob. 99ECh. R.2 - Write each fraction as a percent. See Example 11....Ch. R.2 - Prob. 101ECh. R.2 - Write each fraction as a percent. See Example 11....Ch. R.2 - Prob. 103ECh. R.2 - Write each fraction as a percent. See Example 11....Ch. R.2 - Write each fraction as a percent. See Example 11....Ch. R.2 - Prob. 106ECh. R.2 - Solve each problem. See Example 12.
107. What is...Ch. R.2 - Prob. 108ECh. R.2 - Solve each problem. See Example 12. What is 6% of...Ch. R.2 - Prob. 110ECh. R.2 - Solve each problem. See Example 12.
111. What is...Ch. R.2 - Solve each problem. See Example 12. What is 26% of...Ch. R.2 - Solve each problem. See Example 12.
113. Elwyn’s...Ch. R.2 - Prob. 114ECh. R.2 - Solve each problem. See Example 12. Find the...Ch. R.2 - Prob. 116ECh. R.2 - Prob. 117ECh. R.2 - Prob. 118ECh. R.2 - Prob. 119ECh. R.2 - Prob. 120E
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- 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
- 4. In a study of how students give directions, forty volunteers were given the task ofexplaining to another person how to reach a destination. Researchers measured thefollowing five aspects of the subjects’ direction-giving behavior:• whether a map was available or if directions were given from memory without a map,• the gender of the direction-giver,• the distances given as part of the directions,• the number of times directions such as “north” or “left” were used,• the frequency of errors in directions.a) Identify each of the variables in this study, and whether each is quantitative orqualitative. For each quantitative variable, state whether it is discrete or continuousb) Was this an observational study or an experimental study? Explain your answerarrow_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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