Question

4. Which of the follows are vector spaces? Prove or disprove. (a) The set {x =...

4. Which of the follows are vector spaces? Prove or disprove.

(a) The set {x = αz | α ∈ R, z = (4, 6)T }.

(b) The set of all 3 × 3 matrices which have all negative elements

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x,...
Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x, y) ∈ R if and only if x + 2 > y. For example, (4, 3) is in R because 4 + 2 = 6, which is greater than 3. (a) Is the relation reflexive? Prove or disprove. (b) Is the relation symmetric? Prove or disprove. (c) Is the relation transitive? Prove or disprove. (d) Is it an equivalence relation? Explain.
We have learned that we can consider spaces of matrices, polynomials or functions as vector spaces....
We have learned that we can consider spaces of matrices, polynomials or functions as vector spaces. For the following examples, use the definition of subspace to determine whether the set in question is a subspace or not (for the given vector space), and why. 1. The set M1 of 2×2 matrices with real entries such that all entries of their diagonal are equal. That is, all 2 × 2 matrices of the form: A = a b c a 2....
For Problems #5 – #9, you willl either be asked to prove a statement or disprove...
For Problems #5 – #9, you willl either be asked to prove a statement or disprove a statement, or decide if a statement is true or false, then prove or disprove the statement. Prove statements using only the definitions. DO NOT use any set identities or any prior results whatsoever. Disprove false statements by giving counterexample and explaining precisely why your counterexample disproves the claim. ********************************************************************************************************* (5) (12pts) Consider the < relation defined on R as usual, where x <...
5. Prove or disprove the following statements: (a) Let R be a relation on the set...
5. Prove or disprove the following statements: (a) Let R be a relation on the set Z of integers such that xRy if and only if xy ≥ 1. Then, R is irreflexive. (b) Let R be a relation on the set Z of integers such that xRy if and only if x = y + 1 or x = y − 1. Then, R is irreflexive. (c) Let R and S be reflexive relations on a set A. Then,...
Suppose V and W are two vector spaces. We can make the set V × W...
Suppose V and W are two vector spaces. We can make the set V × W = {(α, β)|α ∈ V,β ∈ W} into a vector space as follows: (α1,β1)+(α2,β2)=(α1 + α2,β1 + β2) c(α1,β1)=(cα1, cβ1) You can assume the axioms of a vector space hold for V × W (A) If V and W are finite dimensional, what is the dimension of V × W? Prove your answer. Now suppose W1 and W2 are two subspaces of V ....
1)T F: All (x, y, z) ∈ R 3 with x = y + z is...
1)T F: All (x, y, z) ∈ R 3 with x = y + z is a subspace of R 3 9 2) T F: All (x, y, z) ∈ R 3 with x + z = 2018 is a subspace of R 3 3) T F: All 2 × 2 symmetric matrices is a subspace of M22. (Here M22 is the vector space of all 2 × 2 matrices.) 4) T F: All polynomials of degree exactly 3 is...
1. A function + : S × S → S for a set S is said...
1. A function + : S × S → S for a set S is said to provide an associative binary operation on S if r + (s + t) = (r + s) +t for all r, s, t ∈ S. Show that any associative binary operation + on a set S can have at most one “unit” element, i.e. an element u ∈ S such that (*) s + u = s = u + s for all...
Prove or disprove the following statements. a) ∀a, b ∈ N, if ∃x, y ∈ Z...
Prove or disprove the following statements. a) ∀a, b ∈ N, if ∃x, y ∈ Z and ∃k ∈ N such that ax + by = k, then gcd(a, b) = k b) ∀a, b ∈ Z, if 3 | (a 2 + b 2 ), then 3 | a and 3 | b.
Define p to be the set of all pairs (l,m) in N×N such that l≤m. Which...
Define p to be the set of all pairs (l,m) in N×N such that l≤m. Which of the conditions (a), (c), (r), (s), (t) does p satisfy? (a) For any two elements y and z in X with (y,z)∈r and (z,y)∈r, we have y=z .(c) For any two elements y and z in X, we have (y,z)∈r or (z,y)∈r. (r) For each element x in X, we have (x,x)∈r. (s) For any two elements y and z in X with...
5. Let S be the set of all polynomials p(x) of degree ≤ 4 such that...
5. Let S be the set of all polynomials p(x) of degree ≤ 4 such that p(-1)=0. (a) Prove that S is a subspace of the vector space of all polynomials. (b) Find a basis for S. (c) What is the dimension of S? 6. Let ? ⊆ R! be the span of ?1 = (2,1,0,-1), ?2 =(1,2,-6,1), ?3 = (1,0,2,-1) and ? ⊆ R! be the span of ?1 =(1,1,-2,0), ?2 =(3,1,2,-2). Prove that V=W.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT