A = Find the matrix A of the linear transformation T(f(t)) = 4f' (t) + 3f(t) from P₂ to P₂ with respect to the standard basis for P₂. { 1,t, t²}.

Find the matrix MÂÂ(T) of the linear transformation T(f(t)) = f(2t + 5) from P₂ to P2 with respect to the standard basis {1, t, t²} for P₂. MBB(T) = 000 000 000

Let d : P5(R) → P5(R) denotes the first derivative. Show that d is a linear map. Choose a basis for P5(R) and find the matrix M(d). Use the matrix M(d) to find the derivative of f(x) = −9x^5 + 11x^4 −4x^2 +5x−1.

A Let T be the linear transformation of P2 (F) defined by the formula T(P(x)) = (x + 2)P'(x) − P(x) a) Find the matrix of T in the standard basis (1, x, x²). :