Problem 5. Let P2 be the vector space of polynomials of degree no more than2 and let B be the standard basis for P2, B = {1, t, t^2}. Let T: ℝ^2 → P2 be thetransformation = x yt (x - y)t^2.(1) (5pts) Compute the image of under T and write the result in B-coordinates.(2) (5pts) Show that T is linear.(3) (5pts) Find a basis for RanT, hence write down dim Ran T.
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