Problem 3.6 (Ellipses, eigenvalues, eigenvectors, and volume) Make neat and clearly-labelled sketches (i.e., draw by hand) of the ellipsoid & = {al(x-r.)"P-1(x- are) = 1} for the following sets of parameters: (a) Center re = [0 0]" and P = [1.5 -0.5; -0.5 1.5]. (b) Center re = [1 - 2]" and P = [3 0;01]. (c) Center re = [-2 1] and P = [9 - 2; -2 6]. For each part (a) (c) also compute each pair of eigenvalues and corresponding eigenvectors. (d) Recall the geometrically meaningful property of the determinant of a square real matrix A: its magnitude | det A| is equal to the volume of the parallelepiped P formed by applying A to the unit cube C = {x|0