3. Let V = P3, the vector space of polynomials of degree at most 3 with coefficients in R. Define T: V \rightarrow V, f \mapsto \frac{d f}{d x}+\frac{d^{2} f}{d

x} ) Prove that T is a linear transformation. b) Let B = {1,x, x², x³} and calculate [T]B. O Verify whether or not the function 3x2 + 3x + 4 is in T(V). Calculate dim(ker(T)) and dim(T(V)).