Chapter 8.3, Problem 11E

a)

To determine

To mark:

The given statement “If $y=c_1{\text{v}}_1+c_2{\text{v}}_2+c_3{\text{v}}_3$ and $c_1+c_2+c_3=1$, then y is a convex combination of ${\text{v}}_1,{\text{v}}_2,\text{and}{\text{v}}_{\text{3}}$” is true or false.

b)

To determine

To mark:

The given statement “If S is a nonempty set, then conv S contains some points that are not in S” is true or false.

c)

To determine

To mark:

The given statement “Is S and T are convex sets, then $S\cup T$ is also convex” is true or false.