Provide an Appropriate Response $2 \mathbf { v } _ { 1 } + 2 \mathbf { v } _ { 2 } - 3 \mathbf { v } _ { 3 }$

Multiple Choice

Provide an appropriate response.
-Which of the following statements are true? I: $2 \mathbf { v } _ { 1 } + 2 \mathbf { v } _ { 2 } - 3 \mathbf { v } _ { 3 }$ is an affine combination of the 3 vectors.
II: The affine hull of two distinct points is a plane.
III: If $S = \{ x \}$ , then aff $S = \{ x \}$ .
IV: If a set of vectors in $\mathfrak { R } ^ { \mathrm { n } }$ is linearly independent, then every vector in $\mathfrak { R } ^ { \mathrm { n } }$ can be written as an affine combination of these vectors.

A) II and IV
B) I and II
C) I and III
D) I, III, and IV