Problem 17 Show that the set ll = {x3 - x2 - 5x + 1, -2x2 + 3x, x3 + 3x2 - 4x + 2, -3x2 + 5} is a basis for P3. Problem 18 Consider the linear transformation from R2x2 to R2x2. T(M)-M3 9] -6 91 M. (a) Find the matrix B of T with respect to the standard basis B of R2x2. (b) Find bases of the image and kernel of B. (c) Find bases of the image and kernel of T, and thus determine the rank and nullity of transformation T. Problem 19 In the plane V defined by the equation 2x, + X2 - 2x3 = 0, consider the bases UI = (a1, a2) and B = (b1, b2) a) Find the change of basis matrix S from B to II. b) Write an equation relating the matrix [a1, a2], [b1, b2], and S=Spa