Question

A vector space V and a subset S are given. Determine if S is a subspace...

A vector space V and a subset S are given. Determine if S is a subspace of V by determining which conditions of the definition of a subspace are satisfied. (Select all that apply.)

V = C[−4, 4] and S = P.

S contains the zero vector.

S is closed under vector addition.

S is closed under scalar multiplication.

None of these

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
4. Prove the Following: a. Prove that if V is a vector space with subspace W...
4. Prove the Following: a. Prove that if V is a vector space with subspace W ⊂ V, and if U ⊂ W is a subspace of the vector space W, then U is also a subspace of V b. Given span of a finite collection of vectors {v1, . . . , vn} ⊂ V as follows: Span(v1, . . . , vn) := {a1v1 + · · · + anvn : ai are scalars in the scalar field}...
Determine whether the given set ?S is a subspace of the vector space ?V. A. ?=?2V=P2,...
Determine whether the given set ?S is a subspace of the vector space ?V. A. ?=?2V=P2, and ?S is the subset of ?2P2 consisting of all polynomials of the form ?(?)=?2+?.p(x)=x2+c. B. ?=?5(?)V=C5(I), and ?S is the subset of ?V consisting of those functions satisfying the differential equation ?(5)=0.y(5)=0. C. ?V is the vector space of all real-valued functions defined on the interval [?,?][a,b], and ?S is the subset of ?V consisting of those functions satisfying ?(?)=?(?).f(a)=f(b). D. ?=?3(?)V=C3(I), and...
use the subspace theorem ( i) is it a non-empty space? ii) is it closed under...
use the subspace theorem ( i) is it a non-empty space? ii) is it closed under vector addition? iii)is it closed under scalar multiplication?) to decide whether the following is a real vector space with its usual operations: the set of all real polonomials of degree exactly n.
For a nonempty subset S of a vector space V , define span(S) as the set...
For a nonempty subset S of a vector space V , define span(S) as the set of all linear combinations of vectors in S. (a) Prove that span(S) is a subspace of V . (b) Prove that span(S) is the intersection of all subspaces that contain S, and con- clude that span(S) is the smallest subspace containing S. Hint: let W be the intersection of all subspaces containing S and show W = span(S). (c) What is the smallest subspace...
Complete the proof Let V be a nontrivial vector space which has a spanning set {xi}...
Complete the proof Let V be a nontrivial vector space which has a spanning set {xi} ki=1. Then there is a subset of {xi} ki=1 which is a basis for V. Proof. We will divide the set {xi} ki=1 into two sets, which we will call good and bad. If x1 ≠ 0, then we label x1 as good and if it is zero, we label it as bad. For each i ≥ 2, if xi ∉ span{x1, . ....
Prove that the set V of all polynomials of degree ≤ n including the zero polynomial...
Prove that the set V of all polynomials of degree ≤ n including the zero polynomial is vector space over the field R under usual polynomial addition and scalar multiplication. Further, find the basis for the space of polynomial p(x) of degree ≤ 3. Find a basis for the subspace with p(1) = 0.
Determine if the given set V is a subspace of the vector space W, where a)...
Determine if the given set V is a subspace of the vector space W, where a) V={polynomials of degree at most n with p(0)=0} and W= {polynomials of degree at most n} b) V={all diagonal n x n matrices with real entries} and W=all n x n matrices with real entries *Can you please show each step and little bit of an explanation on how you got the answer, struggling to learn this concept?*
Definition. Let S ⊂ V be a subset of a vector space. The span of S,...
Definition. Let S ⊂ V be a subset of a vector space. The span of S, span(S), is the set of all finite linear combinations of vectors in S. In set notation, span(S) = {v ∈ V : there exist v1, . . . , vk ∈ S and a1, . . . , ak ∈ F such that v = a1v1 + . . . + akvk} . Note that this generalizes the notion of the span of a...
3. Closure Properties (a) Using that vector spaces are closed under scalar multiplication, explain why if...
3. Closure Properties (a) Using that vector spaces are closed under scalar multiplication, explain why if any nonzero vector from R2 or R3 is in a vector space V, then an entire line’s worth of vectors are in V. (b) Why isn’t closure under vector addition enough to make the same statement? 4. Subspaces and Spans: The span of a set of vectors from Rn is always a subspace of Rn. This is relevant to the problems below because the...
Let V be the set of all triples (r,s,t) of real numbers with the standard vector...
Let V be the set of all triples (r,s,t) of real numbers with the standard vector addition, and with scalar multiplication in V defined by k(r,s,t) = (kr,ks,t). Show that V is not a vector space, by considering an axiom that involves scalar multiplication. If your argument involves showing that a certain axiom does not hold, support your argument by giving an example that involves specific numbers. Your answer must be well-written.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT