Proved that dimRn[x] = n+1 (Let Rn[x] be vector space of all polynomials w/ real coefficients...)

[spinos]

Hello could you help me with this problem?

Let \(\displaystyle Rn[x]\) be the vector space of all polynomials with real coefficients of degree at most n . Show that \(\displaystyle dimRn[x]=n+1\)

 

[fresh_42]

You should try to find a basis, i.e. a system of polynomials that span [imath] \mathbb{R}_n[x] [/imath] and that is linearly independent.

 

[khansaheb]

Hello could you help me with this problem?

Let \(\displaystyle Rn[x]\) be the vector space of all polynomials with real coefficients of degree at most n . Show that \(\displaystyle dimRn[x]=n+1\)

Please show us what you have tried and exactly where you are stuck.

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[Steven G]

Can you find a bijection from your space to R^(n+1)? It's a very natural one.