Question

is span(0, u1,u2, u3) = span(u1, u2, u3)

Answer 1

I don't think so,
My logic is let consider P_4 for (0, u1, u2, u3) and P (x) = a*0 + bx +cx^2 +dx^3
and in P_3 (u1, u2,u3) , the P(x) = a +bx +cx^2
so, the first span is not the second one