# Homework Help: Not a Vector Space

1. Jun 2, 2014

### kq6up

1. The problem statement, all variables and given/known data

For each of the following sets, either verify (as in Example 1) that it is a vector space, or show which requirements are not satisfied. If it is a vector space, find a basis and the dimension of the space.

6. Polynomials of degree ≤ 6 with a3 = 3.

2. Relevant equations

N/A

3. The attempt at a solution

I put that it was a vector space with the basis of {1,x,x^2,3*x^3,x^4,x^5,x^6} and dimension of 7. I am not sure why it fails to be a vector space.

Chris

2. Jun 2, 2014

### tms

What happens if you add two members of the given set, or if you multiply a member by a scalar?

3. Jun 2, 2014

### kq6up

I think there is a closure problem because one would not be able to get rid of the 3*x^3 by playing with coefficients.

I will have to think about it a little more.

Chris

4. Jun 2, 2014

### tms

Definitely.

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