Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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Chapter 6.1, Problem 24EQ
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V.
V=ℝ3,
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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 6 Solutions
Linear Algebra: A Modern Introduction
Ch. 6.1 - 13. Finish verifying that is a vector space (see...Ch. 6.1 - In Exercises 14-17, determine whether the given...Ch. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...Ch. 6.1 - Prob. 25EQCh. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...Ch. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...Ch. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...Ch. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...Ch. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...Ch. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...
Ch. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...Ch. 6.1 - Prob. 35EQCh. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...Ch. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...Ch. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...Ch. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...Ch. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...Ch. 6.1 - Prob. 41EQCh. 6.1 - Prob. 42EQCh. 6.1 - In Exercises 24-45, use Theorem 6.2 to determine...Ch. 6.1 - Prob. 44EQCh. 6.3 - Prob. 18EQCh. 6.4 - In Exercises 1-12, determine whether T is a linear...Ch. 6.4 - In Exercises 1-12, determine whether T is a linear...Ch. 6.4 - In Exercises 1-12, determine whether T is a linear...Ch. 6.4 - In Exercises 1-12, determine whether T is a linear...Ch. 6.4 - In Exercises 1-12, determine whether T is a linear...Ch. 6.4 - Prob. 6EQCh. 6.4 - Prob. 7EQCh. 6.4 - In Exercises 1-12, determine whether T is a linear...Ch. 6.4 - Prob. 9EQCh. 6.4 - In Exercises 1-12, determine whether T is a linear...Ch. 6.4 - Prob. 11EQCh. 6.4 - Prob. 12EQCh. 6.5 -
35. Let T: V→ W be a linear transformation...Ch. 6.7 - In Exercises 1-12, find the solution of the...Ch. 6.7 - Prob. 2EQCh. 6.7 - In Exercises 1-12, find the solution of the...Ch. 6.7 - Prob. 4EQCh. 6.7 - Prob. 5EQCh. 6.7 - Prob. 6EQCh. 6.7 - Prob. 7EQCh. 6.7 - In Exercises 1-12, find the solution of the...Ch. 6.7 - In Exercises 1-12, find the solution of the...Ch. 6.7 - In Exercises 1-12, find the solution of the...Ch. 6.7 - In Exercises 1-12, find the solution of the...Ch. 6.7 - In Exercises 1-12, find the solution of the...
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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
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