Answered: V₁ = {(₁, 2₂,...,xn) € R¹ | x₁ ≥ 0}. V₂… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section: Chapter Questions

Problem 5RQ

See similar textbooks

Related questions

Question

section (i)~(iii)

Problem 4. Let n ≥ 3. Identify which of the following subsets are subspaces of the R-vector
space R". Give brief justifications for your answers.
(i) V₁ = {(₁,
2,...,xn) € R₂ | ₁ ≥ 0}.
(ii) V₂ = {(₁,
2,..., In) € R¹ | 1₁ + 3x₂ = x3}.
(iii) V3 = {(x1, x2,...,xn) € R¹ | x² + 9x² = x²}.
(iv) V₁ = {(₁,
2,...,xn) € R¹ | I₁*₂ = 0}.
2,...,xn) € R¹ | 1₂ € Q}.
(v) V5 = {(₁,
(vi) V6 = {(₁,
2,..., In) € R¹ | TX₂ € Q}.

Expert Solution

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Suppose U and W are two-dimensional subspaces of R3. Show that U∩W≠{0}
10.Suppose that each of the vectors x(1), …, x(m) has n components, where n < m. Show that x(1), …, x(m) are linearly dependent. In each of Problems 11 and 12, determine whether the members of the given set of vectors are linearly independent for −∞ < t < ∞ . If they are linearly dependent, find the linear relation among them.
Do questions 53 and 54 Show if it is a subspace using these 3 steps: 1. has to be equal to the 0 vector 2. has to be closed under addition 3. has to be closed under mulitplication
Suppose that S1 and S2 are subspaces of a vector space (V, F). Show that their intersection S1 ∩ S2 is also a subspace of (V, F). Is their union S1 ∪ S2 always a subspace?
9. Show that P2 (polynomials of degree ≤ 2) is a subspace of P3 (polynomials of degree ≤ 3).
Problem 3: (2 marks) Let V = R be a vector space and let W be a subset of ', where W = {a,b,c):b = c² }. Determine, whether W is a subspace of vector space or not.
This problem finds the curve y=C + D * 2^t which gives the best least squares fit to the points (t,y) = (0,6) , (1,4) , (2,0). Find the coefficents C and D of the best curve y=C + D * 2^t
Which of the following are vector subspaces of R3? all vectors of the form (a, b, c), where b = a + c? all vectors of the form (a, b, c), where b = a + c + 1? Note: In the image the problem is described more clearly, do not skip any step and solve the two parts a and b.
the subset H={(x,y,z)∈ℝ³∣ 2x+3y-3z=4} it can be assured: * if u ∈H, v∈H , then u⊕v∈H* if u∈H, then c⊙u∈H, for all c∈R * H is a subspace of V=ℝ³ answer in each one if it is: False, true or cannot be established.
Show {s,t,4s-3t)|s and t are in ℝ} is a subspace of ℝ3.
QUESTION 1Show that W = {(a, 0, b)|a, b ∈ R} is a subspace of R3

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS