To be a basis it must span and be linearly independent.
The polynomials span the vector
space of since each p in can be
written as which is a
linear combination of .
. The basis has n+1 vectors. In other words, it has dimension 11.
My text is not helping at all and the wikipedia explanations of the concepts: basis and dimension are way over my head.
Let V be the space of polynomials in x and y of degree <= 10. Specify a basis of V and compute dimV.