(2x - y 29. The linear transformation 7: 12 - R3 is given by T (y ) = | x + 3y xty a. T (3) = b. Give the standard matrix for T. 30. B = {x - 4, 2x2 - x + 2 } is a basis for the subspace H of P2, and f (x) E H. a. Suppose [f (x)Is = ()- f(x) = b. Determine whether x2 E H. 31. The linear transformation T (y) = (3 1) (y) transforms a given circle of radius 5 cm the xy plane into an ellipse in the xy plane. What is the area of the ellipse? 32. Use a determinant to find the area of the parallelogram with vertices (3,5), (1,1), (-2,4) and (0,8). 33. Give the system of linear equations that must be solved to find the interpolating polynomial of degree 2 for the points (-1,6), (1,12) and (2,6). DO NOT SOLVE THE SYSTEM. 34. The linear transformation T: P2 - P2 is given by T(f(x)) = (x + 2)-# f(x) - 3f(x). a. T(x - x +4) = b. Set up a system of 3 equations and 3 unknowns to find a function f(x) 6 Pz that solves T(f (x)) = x2 - x + 1. DO NOT SOLVE THE SYSTEM. ( 2x - y = 3 35. Use Cramer's rule to solve the system (2x + 4y = -1) 36. T: 12 - R2 is the linear transformation that rotates points (x, y) counter clockwise around the origin through an angle n/4. Give the matrix A so that T (y) = A ()