or Problems 34–37, determine whether the linear transformation T is invertible. Either formally prove that your nswer is correct, or justify your answer by invoking appropriate definitions and theorems to explain the significance f any calculations you do. Clearly state your final answer. a +b а —b T:R² → M2x2 (R) defined by T(a, b) = ( 2а — b 2а + b

Let T : P2 → P, be the linear transformation such that T(2x) = 2x? – 3x, T(0.5x – 4) = -2x – 4x + 3, T(4x² + 1) = –4x + 4. %3D Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers. T(1) = T(x) = T(x²) = T(ax? + bx + c) =

Section 3.2:Number 6(d, f)only

6. Determine if the linear transformation T(x1, x2, x3) = (2x1 — X2, —X1 − 2x2 + x3, x1 − 3x2 + x3) is (a) one-to-one (b) onto Hint: use your answer from problem 4.