Let v1 = v2 = v3 = {v1, v2, v3}.a. Show that the set S is

Chapter 8, Problem 15E

(choose chapter or problem)

Problem 15E

Let v1 = v2 = v3 = {v1, v2, v3}.

a. Show that the set S is affinely independent.

b. Find the barycentric coordinates of

p1 =

P2 = p3 =  p4 =  and p5 =

with respect to S.

c. Let T be the triangle with vertices v1, v2, and v3. When the sides of T are extended, the lines divide R2 into seven regions. See Fig. 8. Note the signs of the barycentric coordinates of the points in each region. For example, p5 is inside the triangle T and all its barycentric coordinates are positive. Point p1 has coordinates (–, +, +) Its third coordinate is positive because p1 is on the v3 side of the line through v1 and v2. Its first coordinate is negative because p1 is opposite the v1 side of the line through v2 and v3. Point p2 is on the v2v3 edge of T . Its coordinates are (0, +, +). Without calculating the actual values, determine the signs of the barycentric coordinates of points p6, p7, and p8 as shown in Fig. 8.