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vcb003104

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1. Homework Statement

Let S be the following subset of the vector space P3 of all real polynomials p of degree at most 3:

S = {p∈P3|p(1)=0,p'(1) = 0}

where p' is the derivative of p.

I need to first:

Determine whether S is a subspace of P3

Determine whether the polynomial q(x) = x - 2[itex]x^{2}[/itex] + [itex]x^{3}[/itex] is an element of S

2. Homework Equations

S = {p∈P3|p(1)=0,p'(1) = 0}

3. The Attempt at a Solution

How can I prove that it is a subspace?

I know that there are the axioms but how do I use it?

I.E. when I say

u is an element of V

v is an element of V

u+v is an element of V (How do I show it?)

Let S be the following subset of the vector space P3 of all real polynomials p of degree at most 3:

S = {p∈P3|p(1)=0,p'(1) = 0}

where p' is the derivative of p.

I need to first:

Determine whether S is a subspace of P3

Determine whether the polynomial q(x) = x - 2[itex]x^{2}[/itex] + [itex]x^{3}[/itex] is an element of S

2. Homework Equations

S = {p∈P3|p(1)=0,p'(1) = 0}

3. The Attempt at a Solution

How can I prove that it is a subspace?

I know that there are the axioms but how do I use it?

I.E. when I say

u is an element of V

v is an element of V

u+v is an element of V (How do I show it?)

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