Let $W$ is a set of functions with degree at most 1, and so $W_1=\{a_0 +a_1 \cdot x | a_0,a_1 \in \mathbb{R} \}$
I know that the basis of this is the set $B_1 = \{1,x\}$. But I am having trouble showing linearly independance. I know we choose scalers $c_1, c_2$ such that $c_1(1) + c_2(x) = 0$ but I dont know where to go from here. Also I know the dimension is 2 but why is this? Is this because the number of elements in the basis is 2 or because dim(W) = n+1 for polynomials.