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Saurabh Asked a Question
June 11, 2022 7:53 am 10 pts
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
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