(a) Let S be the parallelogram with vertices (3, 0), (9,1), (0,3), and (6,4) in R2. Find the area of S using determinants. Hint: you will first want to find the vectors that represent the edges of the parallelogram (b) Let T : R2 → R2 be the linear transformation given by the standard matrix A 3 -4 Compute the area of the image of S under T (c) Suppose a rectangle R has vertices (0,0), (0,5), (x, 0), and (x,5). If the area of the image of R under T is found to be 10, what is the value of x? (d) Use determinants to find the volume of the parallelepiped in R3 with one vertex at the origin and adjacent vertices at (1, 4,0), (-2,-5,2), and (-1,2,-1) (e) Use determinants to find the area bounded by the ellipse : x2 +y2-1X and let D denote the unit Hint: Let C denote the unit circle: C = disc bounded by C. What is the area of the disc D? Consider the linear transformation T : R2 → R2 given by the rule T(x) = Ax, where A is the matrix A = C underT is the ellipse computing T(x) for some vectors x that represent coordinates of points on the unit circle, but 3 0 The image of -1. You should try to convince yourselves this is true by