Question

Let ℙn be the set of real polynomials of degree at most n, and write p′...

Let ℙn be the set of real polynomials of degree at most n, and write p′ for the derivative of p. Show that

S={p∈ℙ9:p(2)=−1p′(2)}

is a subspace of ℙ9.

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
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.
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.
Let V be the set of polynomials of the form ax + (a^2)(x^2), for all real...
Let V be the set of polynomials of the form ax + (a^2)(x^2), for all real numbers a. Is V a subspace of P?
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.
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.
Let Poly3(x) = polynomials in x of degree at most 2. They form a 3- dimensional...
Let Poly3(x) = polynomials in x of degree at most 2. They form a 3- dimensional space. Express the operator Q(p) = xp' + p'' . as a matrix (i) in basis {1, x, x^2 }, (ii) in basis {1, x, 1+x^2 } . Here, where p(x) represents a polynomial, p’ is its derivative, and p’’ its second derivative.
Let P and Q be polynomials of degree at least one and let a be the...
Let P and Q be polynomials of degree at least one and let a be the lead coefficient of P and b be the lead coefficient of Q. Prove that lim as n approaches infinity of P(n)/Q(n) = 0 deg Q > deg P a/b deg Q = deg P infinity deg Q < deg P
Let H be the set of all polynomials of the form p(t) = at2 where a...
Let H be the set of all polynomials of the form p(t) = at2 where a ∈ R with a ≥ 0. Determine if H is a subspace of P2. Justify your answers.
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?*
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...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT