Which ones of the following subsets of $\displaystyle \mathbb{R}^n$ are subspaces.

a) $\displaystyle L=\{x= \[\alpha_1,\ldots,\alpha_n\]^\top\ | \sum_{i=1}^n (-1)^n\alpha_i =0\} $

b) $\displaystyle M=\{x= \[\alpha_1,\ldots,\alpha_n\]^\top\ | \alpha_i - \alpha_{i-1} = constant\\ i= 2,3,\dots,n\} $

c) $\displaystyle N=\{x= \[\alpha_1,\ldots,\alpha_n\]^\top\ | \left\frac{\alpha_i}{\alpha_{i-1}} \right = constant\\ i= 2,3,\dots,n\} $

d) $\displaystyle P=\{x= \[\alpha_1,\ldots,\alpha_n\]^\top\ | \sum_{i=1}^n 2^{n-1}\alpha_i =0\} $

I should decide their dimensions and give a basis for each. I think a) and d) are subspaces, how can I find the dimension of these spaces and how can I give a basis?

Thank you!