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Let T: P2 -P3 be the transformation that maps a polynomial p(t) into the polynomial (t - 3)p(t). a. Find the image of p(t) = 4 -t + 3t. b. Show that T is a linear transformation. c. Find the matrix for T relative to the following bases B and C. B = { b1 , b2, b3} = { 1, t, t }; C= {C1, C2, C3, CA} = {1, t, + 2, + 3 } a. The image of p(t) = 4 - t + 312 is]. b. Let p(t) and q(t) be polynomials in P2. Show that T(p(t) + q(t)) = T(p(t)) + T(q(t)). T (p(t) + q(t)) Apply the definition of T. Distribute. Apply the definition of T again. Let p(t) be a polynomial in PP2 and let c be a scalar. Show that T(c . p(t)) = c . T(p(t)), thus completing the demonstration that T is a linear transformation. T(c . p(t)) Apply the definition of T. Rearrange the factors. Apply the definition of T again. c. The matrix for T relative to B and C is