Question

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.

Homework Answers

Know the answer?
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
Similar Questions
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).
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 P be the vector space of all polynomials in x with real coefficients. Does P...
Let P be the vector space of all polynomials in x with real coefficients. Does P have a basis? Prove your answer.
Let P(R) denote the family of all polynomials (in a single variable x) with real coefficients....
Let P(R) denote the family of all polynomials (in a single variable x) with real coefficients. We have seen that with the operations of pointwise addition and multiplication by scalars, P(R) is a vector space over R. Consider the 2 linear maps D, I : P(R) to P(R), where D is differentiation and I is anti-differentiation. In detail, for a polynomial p = a0+a1x1+...+anxn, we have D(p) = a1+2a2x+....+nanxn-1 and I(p) = a0x+(a1/2)x2+...+(an/(n+1))xn+1. a. Show that D composed with I...
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?*
Prove that the singleton set {0} is a vector subspace of the space P4(R) of all...
Prove that the singleton set {0} is a vector subspace of the space P4(R) of all polynomials of degree at most 3 with real coefficients.
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.
Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree​ 4; ​...
Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree​ 4; ​ zeros:-5+3i, -4 multiplicity 2 please show all steps and explain
Let R[x] be the set of all polynomials (in the variable x) with real coefficients. Show...
Let R[x] be the set of all polynomials (in the variable x) with real coefficients. Show that this is a ring under ordinary addition and multiplication of polynomials. What are the units of R[x] ? I need a legible, detailed explaination