Let

a. Show that the set S is affinely independent.

b. 

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 Figure 8. 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 Figure 8.

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v₁ = [-2]· 12²= [4]· v² = [8] · VI V2 V3 {V1, V2, V3}. and let S =