What is the dimension of Ropf2 Prove your answer by finding

What is the dimension of Ropf^2? Prove your answer by finding a basis and proving it is a basis.

Solution

Consider R2, the vector space of all coordinates (a, b) where both a and b are real numbers. Then a very natural and simple basis is simply the vectors e1 = (1,0) ande2 = (0,1): suppose that v = (a, b) is a vector in R2, then v = a(1,0) + b(0,1). But any two linearly independent vectors, like (1,1) and (1,2), will also form a basis of R2. so dimension of R2=2