a. Show that the line through vectors p and q in ?n may be written in the parametric form . (Refer to the figure with Exercises 21 and 22 in Section 1.5.)b. The line segment from p to q is the set of points of the form (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. Exercises 21Find a parametric equation of the line M through p and q. [Hint: M is parallel to the vector q – p. See the figure below.] Exercises 22Find a parametric equation of the line M through p and q. [Hint: M is parallel to the vector q – p. See the figure below.]

Solution Step 1:1. The sketch of the line M through vectors p and q in n is shown as follows From the figure it is observed that the line M going through the point p and q is in the direction of q-p So,the equation of line will be of the form