Question

6. Are the following vector spaces over R. (c) RQ (irrational numbers) (а) Q (d) V {(, y) E R2: y 2 (Ъ) М, (R) (e) R2 however

0 0
Add a comment Improve this question Transcribed image text
Answer #1

Is not a Vechu ace aveuR, JiO 2 ER And Cat NE @ en v2x¢&_ e esnoトderd wndeualau muiplicahen Mr(TR)isa yech ae evuR. t A,kENal

Add a comment
Know the answer?
Add Answer to:
6. Are the following vector spaces over R. (c) RQ (irrational numbers) (а) Q (d) V...
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • Question 1: Vector Spaces and Subspaces (a) Show that (C(0, 1]), R, +,), the set of...

    Question 1: Vector Spaces and Subspaces (a) Show that (C(0, 1]), R, +,), the set of continuous functions from [0, 1 to R equipped with the usual function addition and scalar multiplication, is a vector space. (b) Let (V, K, +,-) be a vector space. Show that a non-empty subset W C V which is closed under and - necessarily contains the zero vector. (c) Is the set {(x,y)T: z,y E R, y a subspace of R2? Justify.

  • (4) Let V and W be vector spaces over R: consider the free vector space F(V × W) on the Cartesian...

    (4) Let V and W be vector spaces over R: consider the free vector space F(V × W) on the Cartesian product V x W of V and W. Given an element (v, w) of V x W, we view (v, w) as an element of F(V x W) via the inclusion map i : V x W F(V x W) Any element of F(V x W) is a finite linear combination of such elements (v, w) Warning. F(V ×...

  • help with p.1.13 please. thank you! Group Name LAUSD Health N Vector Spaces P.1.9 Let V...

    help with p.1.13 please. thank you! Group Name LAUSD Health N Vector Spaces P.1.9 Let V be an F-vector space, let wi, W2,...,W, EV, and suppose that at least one w; is nonzero. Explain why span{w1, W2,...,w,} = span{w; : i = 1,2,..., and W; 0). P.1.10 Review Example 1.4.8. Prove that U = {p EP3 : p(0) = 0) is a subspace of P3 and show that U = span{z.z.z). P.1.11 State the converse of Theorem 1.6.3. Is it...

  • just part c,d, and e please!! Let V be a finite-dimensional vector space over F. For...

    just part c,d, and e please!! Let V be a finite-dimensional vector space over F. For every subset SCV, define Sº = {f eV" f(s) = 0 Vs ES}. (a) Prove that sº is a subspace of V* (S may not be a subspace!) (b) If W is a subspace of V and r & W, prove that there exists an few with f(x) +0. (c) If v inV, define u:V* → F by 0(f) = f(v). (This is linear...

  • Q5 (a) Provide the definition of the derivative of a map F: ViV2 where (V, l1) a are normed vector spaces (possibly...

    Q5 (a) Provide the definition of the derivative of a map F: ViV2 where (V, l1) a are normed vector spaces (possibly infinite dimensional) (b) Let C((0, 1) be the space of continuous real valued functions on [0, 1] endowed with the supremum norm. Define F:C ((0, 1]) C([0, 1]) by F(() Jo f()dt, e for all f E C(0, 1). Show directly from the definition that the derivative of F is differentiable on the entire domain. (c) For the...

  • Let V be R2, the set of all ordered pairs (x, y) of real numbers. Define...

    Let V be R2, the set of all ordered pairs (x, y) of real numbers. Define an operation of "addition" by (u, v) @ (x, y) = (u + x +1, v + y + 1) for all (u, v) and (x, y) in V. Define an operation of "scalar multipli- cation" by a® (x, y) = (ax, ay) for all a E R and (x,y) E V Under the two operations the set V is not a vector space....

  • VECTOR SPACES LINEAR ALGEBRA Let V be the set of all ordered pairs of real numbers,...

    VECTOR SPACES LINEAR ALGEBRA Let V be the set of all ordered pairs of real numbers, and consider the following addition and scalar multiplication operations on u = (u1, u2) and v = (v1, v2): u + v = (u1 + v1 + 1, u2 + v2 + 1), ku = (ku1, ku2) a) Show that (0,0) does not = 0 b) Show that (-1, -1) = 0 c) Show that axiom 5 holds by producing an ordered pair -u...

  • Problem 6-20 points. This question is about vector spaces and subspaces. (a) Define the terms "vector...

    Problem 6-20 points. This question is about vector spaces and subspaces. (a) Define the terms "vector space" and "subspace" as precisely as you can. (b) Consider a line through the origin in R2, for example, the r-axis. Explain why this line is, or is not, a subspace of R2 in terms of your definitions in (a). (c) Consider the union of two lines through the origin in R2, for example, the z- and y-axes. Explain why this union of lines...

  • Let V and W be finite dimensional vector spaces over R and T:V + W be...

    Let V and W be finite dimensional vector spaces over R and T:V + W be linear. Let V be a subspace of V and Wo = T(V). (Select ALL that are TRUE) If T is surjective then Vo = {v EV : there is w E Wo such that T(v) = w} If T is injective then dim(VO) = dim(W). dim(ker(T) n Vo) = dim(VO) - dim(Wo).

  • Exercise 15. Are the following functions norms on the vector spaces they are defined? Prove your...

    Exercise 15. Are the following functions norms on the vector spaces they are defined? Prove your answer. (i 21 - 3|r2 for x - (71 12)Т € R?. (1x2)f(x)|d for f(x) e C[0, 1] (i) _ (iii) pl dо + 2la| + 3/az| for p(z) — аz2? + ајя + ao є Pз. Exercise 15. Are the following functions norms on the vector spaces they are defined? Prove your answer. (i 21 - 3|r2 for x - (71 12)Т €...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT