## Rank and nullity

Hi, i'm having trouble with the following question.

In this question
Pn denotes the space of real polynomials of
degree
n or less. Find the rank and nullity of the following
linear maps.

(a)
D : P5 P5, where (Dp)(t) = p(t) + p(t),
(b)
D2, where D is defined as in 3a,
(c)
E : P5 P5, where (Ep)(t) = p(t + 2),

(d)
S : P5 P10, where (Sp)(t) = p(t2 + 1).

Any help would be greatly appreciated.

Thanks.