Define T:P,-R as shown to the right. P(- 1) a. Find the image under T of p(t) = - 2-t b. Show that Tis a linear transformation. c. Find the matrix for T relative to the basis B= (b,, b2. b) = (1, t, ) for Pz and the standard basis E= (e,. e2. e3) for R. T(p) = P(0) P(1) a. The image under Tof p() -2-tis b. Let p(t) and q(t) be polynomials in Pz. Show that T(p() + q() = T(p() + T(q(). First apply the definition of T. (p•9)(1) T(p() + q() = (p+ aX0) Next apply the definition of (p + glt), What is the result? (p• q)(- 1) P(- 1)+ q(1) P(t) • q(t) (p+aX1) O A. P(0) + q(0) OB. P() + q() (p+ q)() p(1)+ al- 1) P(1) + q(t) tis ti P(1) • q(1) P(- 1)• q(- 1) (p+aX- 1) Oc. P(0) + q(0) OD. P(0) + q(0) (p+ gX0) p(- 1)+ q(- 1) P(1) + q(1) (p+ aX1) Rewrite this as the sum of two vectors. What is the result? P(1) P(- 1) 9(- 1) O A. P() OB. P(0) q(0) P(t) P(1) 9(1) P(1) q(1) P(- 1) 9(1) Oc. P(0) q(0) OD. P(0) q(0) P(- 1) 9- 1) P(1) q( - 1)

Q. 3. A transformation T: R² →R² first reflects vectors through the y axis, and then rotates vectors by 3 a. Find the matrix of the transformation T. b. Find the inverse transformation of T , if exists. -1 c. Draw the transformation T for x =| 2