Q3. Recall that P, is the vector space of all real polynomials of degree at most...

Question

Question

Q3. Recall that P, is the vector space of all real polynomials of degree at most n. Determine whether the following subset of

Answer 1

Answer #1

Yes H= { plt) Pn 1 bit)=0} is a subspace of Pn. Take Þi , B2 E H Then it means Bit) = p lt) 20 Now (P. +bz) = pi + b (as de

Answer 2

Similar Homework Help Questions

Q3. Recall that P, is the vector space of all real polynomials of degree at most...

Q3. Recall that P, is the vector space of all real polynomials of degree at most n. Determine whether the following subset of P, is a subspace: H = {p(t) € Pn such that p'(t)=0}, where p' (t) is the derivative of the polynomial p(t).
Let P3 be the vector space of all real polynomials of degree at most 3. Determine whether S is a ...

Let P3 be the vector space of all real polynomials of degree at most 3. Determine whether S is a subspace of P3, where S
Q3. Consider the vector space P, consisting of all polynomials of degree at most two together...

Q3. Consider the vector space P, consisting of all polynomials of degree at most two together with the zero polynomial. Let S = {p.(t), p2(t)} be a set of polynomials in P, where: pi(t) = -4 +5, po(t) = -3° - 34+5 (a) Determine whether the set S = {P1(t).pz(t)} is linearly independent in Py? Provide a clear justification for your solution. (8 pts) (b) Determine whether the set S = {p(t),p2(t)} spans the vector space P ? Provide a...

Recall that P2 is the vector space of all polynomials of degree at most 2. Given...

Recall that P2 is the vector space of all polynomials of degree at most 2. Given U = Span({3+t?, t, 3t – 2,5t +t+1}), find the dimension of U as a subspace of P2.
Q3. Consider the vector space B, consisting of all polynotninls of degree at most two together...

Q3. Consider the vector space B, consisting of all polynotninls of degree at most two together with the zero polynomial. Let S = {p(t).p2(t)} be a set of polynomials in P, where P.(t) = -2+3 pa(t) --21-24 + 3 (a) Determine whether the set S = {p(), pea(t)} is linearly independent in Py? Provide a clear justification for your solution. (8 pts) (b) Determine whether the set S = {p(t), pa(t)} spans the vector space B? Provide a clear justification...
3. P. is the vector space of all polynomials of degree n or less and the...

3. P. is the vector space of all polynomials of degree n or less and the zero polynomial Define a derivative transformation T as follow: T. +P, T(+241 +0,2%) = 41 + 2121 (a) (10 Puan) Find the corresponding matrix for T. (b) (10 Puan) Choose your polynomial in P, and find the derivative of your polynomial by using the matrix in (a).

Let P2 be the real vector space of polynomials in a of degree at most 2, and let T be the real vector space of upper tr...

Let P2 be the real vector space of polynomials in a of degree at most 2, and let T be the real vector space of upper triangular 2 x 2 matrica b,cERThe vector space P2 is equipped with the inner product 〈p(x), q(x)-1 p(z)q(z) dr, and the vector space T is equipped with the inner product 〈A.B)=tr(AB), where tr denotes trace. Let L: P2→T be 1.p(z)dr]. Find L 0 c given by L(p(z)):-17(1) .CE :J ) 1 2 0 p(-1)...
Let Pn be the set of real polynomials of degree at most n. Show that s (pEP5 :p(-7) (9)) is a sub...

Let Pn be the set of real polynomials of degree at most n. Show that s (pEP5 :p(-7) (9)) is a subspace of P5 Let Pn be the set of real polynomials of degree at most n. Show that s (pEP5 :p(-7) (9)) is a subspace of P5
Given the vector space R[2]deg<s of polynomials with real coefficients of degree at most 5, and...

Given the vector space R[2]deg<s of polynomials with real coefficients of degree at most 5, and Ui = {p(z) : p(z) a? + bz5, for abe R}, find a subspace U2 such that R deg< 5 = Ui φ Ủy Is this U2 unique? (g) If V be a finite dimensional vector space, dim V = n and B = 〈ui,u2, . . . , un) is a basis of V, then show that:

Let P2 be the vector space of all polynomials of degree 2 or less, and let...

Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 8x−5x2+3, 2x-2x2+1 and 3x2-1. a) The dimensions of the subspace H is ___________? b) Is {8x-5x2+3, 2x-2x2+1, 3x2-1} a basis for P2? ________(be sure to explain and justify answer) c) A basis for the subspace H is {_________}? enter a polynomial or comma separated list of polynomials