Find the Barycentric Coordinates of P with Respect to the Affinely

question 50

Multiple Choice

Find the barycentric coordinates of p with respect to the affinely independent set of points that precedes it.
-Which of the following statements are true for the set $S = \left\{ \mathbf { v } _ { 1 } , \ldots , \mathbf { v } _ { \mathrm { k } } \right\}$ in $\mathfrak { R } ^ { n }$ ?
I: $\left\{ \mathbf { v } _ { 2 } - \mathbf { v } _ { 1 } , \ldots , \mathbf { v } _ { \mathrm { k } } - \mathbf { v } _ { 1 } \right\}$ is linearly dependent if and only if $S$ is affinely dependent.
II: If $S$ is affinely independent and a point $p$ in $R ^ { n }$ has all positive barycentric coordinates determined by $S$ , then $p$ is not in aff $S$ .

• A) I
• B) II
• C) Neither I or II
• D) Both I and II

---

Definitions:

Private Property

Land or possessions owned by individuals or corporations rather than by the government or public as a whole.

Public Use

Utilization of land or property by the general public or government entities, often a criterion in eminent domain cases.

Landowners Downstream

Individuals or entities that own property located lower in the watershed or river flow, potentially affected by upstream activities.

Diverting

The act of changing the direction or use of something from its intended course or purpose.