Let A 4 be the R-vector space V = {p € R[x] / degree (p) 3).

(a) Show that B = ((1+x)°, (1+x)1, (1+x)2, (1 + x)3) an ordered basis of V

shall. What is the dimension of V?

(b) Calculate the coordinate vector of p = 2x3 + 5x2 + 4x - 1 with respect to the

Base B.

(3 + 2 Points)