Provide an Appropriate Response
- And $2 \mathbf { v } _ { 1 } + \mathbf { v } _ { 2 } - 2 \mathbf { v } _ { 3 } - \mathbf { v } _ { 4 } = \mathbf { 0 }$

question 39

Multiple Choice

Provide an appropriate response
- $\mathbf { p } = \frac { 1 } { 2 } \mathbf { v } _ { 1 } + \frac { 1 } { 8 } \mathbf { v } _ { 2 } + \frac { 1 } { 8 } \mathbf { v } _ { 3 } + \frac { 1 } { 4 } \mathbf { v } _ { 4 }$ and $2 \mathbf { v } _ { 1 } + \mathbf { v } _ { 2 } - 2 \mathbf { v } _ { 3 } - \mathbf { v } _ { 4 } = \mathbf { 0 }$
Use the procedure in the proof of Caratheodory's Theorem to express $\mathbf { p }$ as a convex combination of three of the $\mathbf { v } _ { \mathbf { i } }$ 's.

• A) \(p = \frac { 5 } { 8 } \mathbf { v } _ { 1 } + \frac { 3 } { 16 } \mathbf { v } _ { 2 } + \frac { 3 } { 16 } \mathbf { v } _ { 4 }\)
• B) \(\mathbf { p } = \frac { 1 } { 4 } \mathbf { v } _ { 1 } + \frac { 3 } { 8 } \mathbf { v } _ { 2 } + \frac { 3 } { 8 } \mathbf { v } _ { 4 }\)
• C) \(\mathrm { p } = \frac { 1 } { 8 } \mathbf { v } _ { 2 } + \frac { 3 } { 8 } \mathbf { v } _ { 3 } + \frac { 1 } { 2 } \mathbf { v } _ { 4 }\)
• D) It cannot be done using only \(3 \mathbf { v } _ { \mathbf { i } }\) 's.

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