Let p2 be the vector space of all polynomials of degree at most 2 over r (the set of real numbers). let a linear transformation t: p2-p2 be defined by t(a +bx +

Let P2 be the vector space of all polynomials of degree at most 2 over R (the set of real numbers). Let a linear transformation T: P2-P2 be defined by T(a +bx + cx²)= (a +b) + (b - c)x + (a + c)x² Consider the foilowing statements: 1. The ull space of T is {α(-1+x + x²) : α∈R}. II. The range space of T is spanned by the set {1+x²,1+x}. III. T(T(1 +x)) = 1 +x² IV. If M is the matrix representation of T with respect to the standard basis {1,x, x²} of P2, then the trace of the matrix M is 3 . Which of the above statements are TRUE? (A) I and II only (B) I. IIl and IV only (C) I, II and IV only (D) II and IV only