College Algebra: Graphs and Models (6th Edition)
6th Edition
ISBN: 9780134179032
Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna
Publisher: PEARSON
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Chapter J.6, Problem 6E
To determine
To write: The interval notation 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 J Solutions
College Algebra: Graphs and Models (6th Edition)
Ch. J.1 - In Exercises 1-6, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.2 - Name the property illustrated by the sentence. 1....Ch. J.2 - Name the property illustrated by the sentence. 2....Ch. J.2 - Name the property illustrated by the sentence. 3....Ch. J.2 - Prob. 4E
Ch. J.2 - Prob. 5ECh. J.2 - Prob. 6ECh. J.2 - Prob. 7ECh. J.2 - Prob. 8ECh. J.2 - Prob. 9ECh. J.2 - Prob. 10ECh. J.3 - Classify the inequality as true or false. 1. 9 9Ch. J.3 - Prob. 2ECh. J.3 - Classify the inequality as true or false. 3. 265Ch. J.3 - Prob. 4ECh. J.3 - Prob. 5ECh. J.3 - Prob. 6ECh. J.4 - Simplify. 1. |98|Ch. J.4 - Prob. 2ECh. J.4 - Prob. 3ECh. J.4 - Prob. 4ECh. J.4 - Prob. 5ECh. J.4 - Prob. 6ECh. J.4 - Prob. 7ECh. J.4 - Prob. 8ECh. J.5 - Compute and simplify. 1. 8 (11)Ch. J.5 - Compute and simplify. 2. 310(13)Ch. J.5 - Prob. 3ECh. J.5 - Prob. 4ECh. J.5 - Prob. 5ECh. J.5 - Prob. 6ECh. J.5 - Prob. 7ECh. J.5 - Prob. 8ECh. J.5 - Prob. 9ECh. J.5 - Prob. 10ECh. J.5 - Prob. 11ECh. J.5 - Compute and simplify. 12. 1223Ch. J.5 - Prob. 13ECh. J.5 - Prob. 14ECh. J.5 - Prob. 15ECh. J.6 - Write interval notation. 1. {x| 5 x 5}Ch. J.6 - Prob. 2ECh. J.6 - Write interval notation. 3. {x | x 2}Ch. J.6 - Write interval notation. 4. {x | x 3.8}Ch. J.6 - Prob. 5ECh. J.6 - Prob. 6ECh. J.6 - Prob. 7ECh. J.6 - Prob. 8ECh. J.6 - Prob. 9ECh. J.6 - Write interval notation for the graph. 10.Ch. J.7 - Simplify. 1. 36Ch. J.7 - Prob. 2ECh. J.7 - Prob. 3ECh. J.7 - Prob. 4ECh. J.7 - Prob. 5ECh. J.7 - Prob. 6ECh. J.7 - Prob. 7ECh. J.7 - Prob. 8ECh. J.7 - Prob. 9ECh. J.7 - Prob. 10ECh. J.8 - Convert to scientific notation. 1. 18,500,000Ch. J.8 - Prob. 2ECh. J.8 - Prob. 3ECh. J.8 - Prob. 4ECh. J.8 - Convert to decimal notation. 5.4.3 108Ch. J.8 - Prob. 6ECh. J.8 - Convert to decimal notation. 7.6.203 1011Ch. J.8 - Prob. 8ECh. J.9 - Calculate. 1. 3 + 18 6 3Ch. J.9 - Calculate. 2. 5 3 + 8 32 + 4(6 2)Ch. J.9 - Calculate. 3. 5(3 8 32 + 4 6 2)Ch. J.9 - Calculate. 4. 16 4 4 2 256Ch. J.9 - Calculate. 5. 26 23 210 28Ch. J.9 - Calculate. 6. 4(86)243+2831+190Ch. J.9 - Calculate. 7. 64 [(4) (2)]Ch. J.9 - Prob. 8ECh. J.10 - Determine the degree of the polynomial. 1. 5 x6Ch. J.10 - Prob. 2ECh. J.10 - Prob. 3ECh. J.10 - Prob. 4ECh. J.10 - Prob. 5ECh. J.10 - Prob. 6ECh. J.10 - Prob. 7ECh. J.10 - Prob. 8ECh. J.11 - Add or subtract. 1. (8y 1) (3 y)Ch. J.11 - Add or subtract. 2. (3x2 2x x3 + 2) (5x2 8x ...Ch. J.11 - Prob. 3ECh. J.11 - Prob. 4ECh. J.11 - Prob. 5ECh. J.12 - Prob. 1ECh. J.12 - Prob. 2ECh. J.12 - Prob. 3ECh. J.12 - Prob. 4ECh. J.12 - Prob. 5ECh. J.12 - Prob. 6ECh. J.13 - Multiply. 1. (x + 3)2Ch. J.13 - Multiply. 2. (5x 3)2Ch. J.13 - Multiply. 3. (2x + 3y)2Ch. J.13 - Prob. 4ECh. J.13 - Multiply. 5. (n + 6) (n 6)Ch. J.13 - Prob. 6ECh. J.14 - Factor out the largest common factor. 1. 3x + 18Ch. J.14 - Prob. 2ECh. J.14 - Prob. 3ECh. J.14 - Prob. 4ECh. J.14 - Prob. 5ECh. J.14 - Prob. 6ECh. J.14 - Prob. 7ECh. J.14 - Prob. 8ECh. J.14 - Prob. 9ECh. J.14 - Prob. 10ECh. J.14 - Prob. 11ECh. J.14 - Prob. 12ECh. J.15 - Factor. 1. 8x2 6x 9Ch. J.15 - Factor. 2. 10t2 + 4t 6Ch. J.15 - Factor. 3. 18a2 51a + 15Ch. J.16 - Factor the difference of squares. 1. z2 81Ch. J.16 - Factor the difference of squares. 2. 16x2 9Ch. J.16 - Factor the difference of squares. 3. 7pq4 7py4Ch. J.16 - Factor the square of a binomial. 4. x2 + 12x + 36Ch. J.16 - Prob. 5ECh. J.16 - Factor the square of a binomial. 6. a3 + 24a2 +...Ch. J.16 - Factor the sum or the difference of cubes. 7. x3 +...Ch. J.16 - Factor the sum or the difference of cubes. 8. m3 ...Ch. J.16 - Prob. 9ECh. J.16 - Prob. 10ECh. J.17 - Prob. 1ECh. J.17 - Prob. 2ECh. J.17 - Prob. 3ECh. J.17 - Prob. 4ECh. J.17 - Solve. 5. 7y 1 = 23 5yCh. J.17 - Prob. 6ECh. J.17 - Prob. 7ECh. J.17 - Solve. 8. 5y 4 (2y 10) = 25Ch. J.18 - Prob. 1ECh. J.18 - Prob. 2ECh. J.18 - Prob. 3ECh. J.18 - Prob. 4ECh. J.18 - Prob. 5ECh. J.18 - Prob. 6ECh. J.19 - Prob. 1ECh. J.19 - Prob. 2ECh. J.19 - Prob. 3ECh. J.19 - Prob. 4ECh. J.19 - Prob. 5ECh. J.19 - Prob. 6ECh. J.19 - Prob. 7ECh. J.19 - Prob. 8ECh. J.20 - Prob. 1ECh. J.20 - Prob. 2ECh. J.20 - Prob. 3ECh. J.20 - Prob. 4ECh. J.20 - Prob. 5ECh. J.20 - Prob. 6ECh. J.21 - Prob. 1ECh. J.21 - Prob. 2ECh. J.21 - Prob. 3ECh. J.21 - Prob. 4ECh. J.21 - Prob. 5ECh. J.21 - Prob. 6ECh. J.22 - Prob. 1ECh. J.22 - Prob. 2ECh. J.22 - Prob. 3ECh. J.22 - Prob. 4ECh. J.22 - Prob. 5ECh. J.22 - Prob. 6ECh. J.23 - Prob. 1ECh. J.23 - Prob. 2ECh. J.23 - Prob. 3ECh. J.23 - Prob. 4ECh. J.23 - Prob. 5ECh. J.23 - Prob. 6ECh. J.24 - Simplify. 1. xyyx1y+1xCh. J.24 - Prob. 2ECh. J.24 - Prob. 3ECh. J.24 - Prob. 4ECh. J.24 - Simplify. 5. abba1a1b Note: b a = 1(a b)Ch. J.25 - Prob. 1ECh. J.25 - Prob. 2ECh. J.25 - Prob. 3ECh. J.25 - Prob. 4ECh. J.25 - Prob. 5ECh. J.25 - Prob. 6ECh. J.25 - Prob. 7ECh. J.25 - Prob. 8ECh. J.25 - Prob. 9ECh. J.25 - Prob. 10ECh. J.25 - Prob. 11ECh. J.25 - Prob. 12ECh. J.25 - Prob. 13ECh. J.25 - Prob. 14ECh. J.25 - Prob. 15ECh. J.25 - Prob. 16ECh. J.25 - Prob. 17ECh. J.25 - Prob. 18ECh. J.25 - Prob. 19ECh. J.25 - Prob. 20ECh. J.26 - Prob. 1ECh. J.26 - Prob. 2ECh. J.26 - Prob. 3ECh. J.26 - Prob. 4ECh. J.26 - Prob. 5ECh. J.26 - Prob. 6ECh. J.26 - Prob. 7ECh. J.26 - Prob. 8ECh. J.27 - Prob. 1ECh. J.27 - Prob. 2ECh. J.27 - Prob. 3ECh. J.27 - Prob. 4ECh. J.27 - Prob. 5ECh. J.27 - Prob. 6ECh. J.27 - Prob. 7ECh. J.27 - Convert to exponential notation. 8. x5Ch. J.27 - Prob. 9ECh. J.27 - Prob. 10ECh. J.27 - Prob. 11ECh. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...
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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
- 5. Solve for the matrix X. (Hint: we can solve AX -1 = B whenever A is invertible) 2 3 0 Χ 2 = 3 1arrow_forwardWrite p(x) = 6+11x+6x² as a linear combination of ƒ (x) = 2+x+4x² and g(x) = 1−x+3x² and h(x)=3+2x+5x²arrow_forward3. Let M = (a) - (b) 2 −1 1 -1 2 7 4 -22 Find a basis for Col(M). Find a basis for Null(M).arrow_forward
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