Question

Question 4. Consider the following subsets of the vector space P3 of polynomials of degree 3...

Question 4. Consider the following subsets of the vector space P3 of polynomials of degree 3 or less: S = {p(x) : p(1) = 0} and T = {q(x) : q(0) = 1} Determine if these subsets are vectors spaces with the standard operations for polynomials

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

Homework Answers

Answer #1

For proving S is vector space, we can also go by long route of proving all properties of vector spaces.

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 P3 = {a + bx + cx2 + dx3 |a,b,c,d ∈ R}, the set of...
Consider P3 = {a + bx + cx2 + dx3 |a,b,c,d ∈ R}, the set of polynomials of degree at most 3. Let p(x) be an arbitrary element in P3. (a) Show P3 is a vector space. (b) Find a basis and the dimension of P3. (c) Why is the set of polynomials of degree exactly 3 not a vector space? (d) Find a basis for the set of polynomials satisfying p′′(x) = 0, a subspace of P3. (e) Find...
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....
If V is a vector space of polynomials of degree n with real numbers as coefficients,...
If V is a vector space of polynomials of degree n with real numbers as coefficients, over R, and W is generated by the polynomials (x 3 + 2x 2 − 2x + 1, x3 + 3x 2 − x + 4, 2x 3 + x 2 − 7x − 7), then is W a subspace of V , and if so, determine its basis.
Let P4 denote the space of polynomials of degree less than 4 with real coefficients. Show...
Let P4 denote the space of polynomials of degree less than 4 with real coefficients. Show that the standard operations of addition of polynomials, and multiplication of polynomials by a scalar, give P4 the structure of a vector space (over the real numbers R). Your answer should include verification of each of the eight vector space axioms (you may assume the two closure axioms hold for this problem).
Let V = Pn(R), the vector space of all polynomials of degree at most n. And...
Let V = Pn(R), the vector space of all polynomials of degree at most n. And let T : V → V be a linear transformation. Prove that there exists a non-zero linear transformation S : V → V such that T ◦ S = 0 (that is, T(S(v)) = 0 for all v ∈ V) if and only if there exists a non-zero vector v ∈ V such that T(v) = 0. Hint: For the backwards direction, consider building...
Let the set W be: all polynomials in P3 satisfying that p(-t)=p(t), Question: Is W a...
Let the set W be: all polynomials in P3 satisfying that p(-t)=p(t), Question: Is W a vector space or not? If yes, find a basis and dimension
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.
Find an inner product on vector space P of polynomials that makes x and y orthogonal....
Find an inner product on vector space P of polynomials that makes x and y orthogonal. (x=1+t, y=1-t)
Let P2 denote the vector space of polynomials in x with real coefficients having degree at...
Let P2 denote the vector space of polynomials in x with real coefficients having degree at most 2. Let W be a subspace of P2 given by the span of {x2−x+6,−x2+2x−1,x+5}. Show that W is a proper subspace of P2.
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.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT