a. Show that the line through vectors p and q in Rn may be written in the parametric form x = (1 - t)p + tq.
b. The line segment from p to q is the set of points of the form (1 - t)p + tq for 0 ≤ t ≤ 1 (as shown in the figure below). Show that a linear transformation T maps this line segment onto a line segment or onto a single point.
