# determining the matrix of a linear transformation (first order derivative) with respect to a basis

Let V be the vector space of all polynomials of degree ≤ $k$.
Let $D:V→V$ be the linear transformation given by $p(x) → p′(x)$ (the derivative).
Determine the matrix of $D$ with respect to the basis $1, x, . . . , x^k$ and determine the rank and nullity of $D$.