I need explanation for this.

The first four Hermite polynomials are 1, 2t, -2 + 4t', and -12t + 8t . Denote b1 = 1, b2 = 2t, b3 = -2 + 4t2, b4 - 12t + 813, and call B = {b1, b2, b3, b4}- 1) Show that B forms a basis of P3 2) Let p(t) = POLYNOMIAL. Find [p] B 3) Find the polynomial f(t) such that [f ]B = Let A = 1) Find a basis for Col(A) and state the dimension of Col(A). 2) Find a basis for Nul(A) and state the dimension of Nul(A). 3) Find a basis for Row(A) and state the dimension of Row(A). 4) Verify that both sentences of our book's rank theorem are true for this example