Define T : P4(R) → P4(R) by T(p)= ((3x^2 −4x+9)p)'' (a) Show that T is a surjective linear map. (b) Find the matrix M(T). (c) Let q(x) = x4 −8x3 +5x2 −x+2. Find p ∈ P4(R) such that T(p) = q by solving...

Define T : P4(R) → P4(R) by
T(p)= ((3x^2 −4x+9)p)''

(a)  Show that T is a surjective linear map.

(b)  Find the matrix M(T).

(c)  Let q(x) = x4 −8x3 +5x2 −x+2. Find p ∈ P4(R) such that T(p) = q by solving the matrix equation M(T)X = M(q) via row reduction