I have the following homework problem, and I just want to clarify if I completed it correctly since it's been a while since I've taken linear algebra. 

Let V be the space of polynomials in $ x$ and $y$ of degree $\leq 10$. Specify a basis of V and compute $dim V$. 

Basis: $[{1, x, y, x^2, y^2, x^3, y^3, x^4,y^4, x^5, y^5,x^6, y^6, x^7, y^7, x^8, y^8, x^9, y^9, x^{10}, y^{10}}]$

$ dim V = 21 $. The dimension is simply the number of elements, correct? 

Is this correct?