Suppose you consider [tex]P_4[/tex] (polynomials of degree at most 4): [tex]A(t)=a_0+a_1t+a_2t^2+a_3t^3+a_4t^4[/tex]

Now if we consider the subspace of these polynomials such that [tex]a_0=0,\ a_1=0,\ a_2=0}[/tex], I propose that the dimension of of this subspace is 2 (versus the dimension of [tex]P_4[/tex] which is 5. Am I incorrect in saying this?

Based on the answer to this I have a follow up question regarding a linear operator on [tex]P_n[/tex]