Q1 4 Points In each part, determine if the given set H is a subspace of the given vector space V. Q1.1 1 Point V=R4 and H is the set of all vectors in R4 which have the form (e.g., the vector x = 園 2 a b x = for some scalars - 2a 1 +36 a, b. is an example of one element of H.) Q1.4 1 Point V=C(R), the vector space of all real-valued continuous functions whose domain is the set R of all real numbers, and H is the subset of C(R) consisting of all of the constant functions. (e.g. the function ƒ : R → R defined by the formula f(x) = 3 for all x E R is an example of one element of H.) OH is a subspace of V. H is not a subspace of V. Save Answer

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
icon
Related questions
Question
Q1
4 Points
In each part, determine if the given set H is a subspace of the given vector space V.
Q1.1
1 Point
V=R4 and H is the set of all vectors in R4 which have the form
(e.g., the vector x =
園
2
a
b
x =
for some scalars
- 2a
1 +36
a, b.
is an example of one element of H.)
Transcribed Image Text:Q1 4 Points In each part, determine if the given set H is a subspace of the given vector space V. Q1.1 1 Point V=R4 and H is the set of all vectors in R4 which have the form (e.g., the vector x = 園 2 a b x = for some scalars - 2a 1 +36 a, b. is an example of one element of H.)
Q1.4
1 Point
V=C(R), the vector space of all real-valued continuous functions whose domain is the set R of
all real numbers, and H is the subset of C(R) consisting of all of the constant functions.
(e.g. the function ƒ : R → R defined by the formula f(x) = 3 for all x E R is an example of one
element of H.)
OH is a subspace of V.
H is not a subspace of V.
Save Answer
Transcribed Image Text:Q1.4 1 Point V=C(R), the vector space of all real-valued continuous functions whose domain is the set R of all real numbers, and H is the subset of C(R) consisting of all of the constant functions. (e.g. the function ƒ : R → R defined by the formula f(x) = 3 for all x E R is an example of one element of H.) OH is a subspace of V. H is not a subspace of V. Save Answer
Expert Solution
steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
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