Determine Whether the Point P Is in the Convex Hull

question 46

Multiple Choice

Determine whether the point p is in the convex hull of S.
- $$\begin{array} { l } \mathrm { S } = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } , \mathbf { v } _ { 4 } \right\} \\\mathbf { v } _ { 1 } = \left[ \begin{array} { l } 2 \\0 \\5 \\1\end{array} \right] , \mathbf { v } _ { 2 } = \left[ \begin{array} { r } 1 \\1 \\- 1 \\- 3\end{array} \right] , \mathbf { v } _ { 3 } = \left[ \begin{array} { r } 3 \\2 \\0 \\- 4\end{array} \right] , \mathbf { p } = \left[ \begin{array} { r } 0 \\- 1 \\4 \\2\end{array} \right]\end{array}$$

• A) \(\mathrm { p } \in \mathrm { conv } \mathrm { S } . \mathrm { p } = \frac { 3 } { 8 } \mathbf { v } _ { 1 } + \frac { 1 } { 4 } \mathbf { v } _ { 2 } + \frac { 3 } { 8 } \mathbf { v } _ { 3 }\)
• B) \(\mathbf { p } \in\) conv S. \(\mathbf { p } = \mathbf { v } _ { 1 } + \mathbf { v } _ { 2 } - \mathbf { v } _ { 3 }\)
• C) \(\mathbf { p } \notin \operatorname { conv } \mathrm { S }\).
• D) \(\mathbf { p } \in\) conv S. \(\mathbf { p } = 2 \mathbf { v } _ { 1 } + 3 \mathbf { v } _ { 2 } - 4 \mathbf { v } _ { 3 }\)

Understand the financial implications of premature settlement proposals on promissory notes and investments.

Evaluate and decide between investment options based on their simple interest yield.

Comprehend the effect of interest rate changes on the profitability of selling investments before maturity.

Calculate the maturity value of notes with given face value, interest rates, and durations.

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