Subspaces, linear dependece/independence Can someone show me how to solve the two following questions. I am doing some exercises for an exam and have other similar problems. 
1) In the linear space of all real polynomials $p(t),$ describe the subspace spanned by each of the the subset $\{1,t^2,t^4 \}$ of polynomials and determine its dimension.
2) Let $V$ be the linear space consisting of all real-valued functions defined on the real line. Determine whether the subset $\{1,e^{ax},e^{bx} \}, a\neq b$ of V is dependent or independent. Compute the dimension of the subspace spanned by $\{1,e^{ax},e^{bx} \}, a\neq b$.
Thank you

The Subspace spanned by $\{1, t^2 , t^4\}$ are all polynomials in the form of 
$$p(x) = a_4 t^4 + a_2 t^2 + a_0$$
where $a_4,a_2,a_0\in \mathbb{R}$ 
As $1$ and $t^2$ and $t^4$ are linear independent the dimension is $3$.
For 2) think about if there is a non trivial solution of 
$$ \alpha \cdot 1 + \beta e^{ax} + \gamma e^{bx}$$ 
when $a\neq b$ (taking the derivative may help) 
