Calculus Linear algebra

Let V = span{e2x, xe2x, x2e2x}.
(a) Show that d/dx (􏰀a1e^2x + a2xe^2x + a3x^2e^2x)􏰁 ∈ V for any a1, a2, a3 ∈ R

(b) let [1 0 0], [0 1 0], and [0 0 1] represent the functions e^2x, xe^2x and x^2e^2x, respectively.
For example, [3 4 5] represents 3e^2x + 4xe^2x + 5x^2e^2x .
Find the matrix of differentiation as a linear transformation on V .

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