Recent content by said

I simply do not see the mistakes that you pointed out. As for the first one, I don't see where I implied that a spanning set of a vector space is a basis. For the second one, I only said that we must show that this subspace is a basis. I did not say it is a basis.

My professor uses the notation <1,α,α2,...> but yes it is a spanning set. So, by proving this, does it automatically prove that the subset of cardinality n is linearly dependent? If yes then what theorem/definition says this? But P(α) = 0 does not tell me anything about linear independence...

Homework Statement [/B] Let α ∈ ℂ be a complex number. Let V = ℚ(α) be the rational vector space spanned by powers of α. That is ℚ(α) = <1,α,α2,...>. 1) If P(t) is a polynomial of degree n such that P(α) = 0, show that dimℚℚ(α) is at most n.Homework EquationsThe Attempt at a Solution...

Let α ∈ ℂ be a complex number. Let V = ℚ(α) be the rational vector space spanned by powers of α. That is ℚ(α) = <1,α,α2,...>. 1) If P(t) is a polynomial of degree n such that P(α) = 0, show that dimℚℚ(α) is at most n.Here is my attempt to solve this question. Please give me some...