Determine If the Vector P Is in Span S or Aff

question 19

Multiple Choice

Determine if the vector p is in Span S or aff S.
- $\text { Let } \mathbf{v}_{1}=\left[\begin{array}{r}2 \\1 \\3 \\-2\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{r}3 \\-1 \\0 \\4\end{array}\right], \mathbf{v}_{3}=\left[\begin{array}{r}5 \\4 \\-1 \\-2\end{array}\right], p=\left[\begin{array}{r}5 \\-3 \\5 \\3\end{array}\right] \text {, and } \mathrm{S}=\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\} \text {. It can be shown that } \mathrm{S} \text { is linearly }$ independent.

• A) \(\mathbf { p } \in\) span \(S\) and \(\mathbf { p } \notin\) aff \(S\)
• B) \(\mathbf { p } \notin \operatorname { span } S\) and \(\mathbf { p } \in\) aff \(S\)
• C) \(\mathbf { p } \in \operatorname { span } S\) and \(\mathbf { p } \in\) aff \(S\)
• D) \(\mathbf { p } \notin \operatorname { span } S\) and \(\mathbf { p } \notin\) aff \(S\)

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Definitions:

Fixed Costs

Expenses that do not change with changes in the volume of production or sales, such as rent, salaries, and insurance.

Operating Leverage

A measure of how revenue growth translates into growth in operating income, indicating the percentage of fixed costs in a company's cost structure.

Financial Break-Even

The point at which total revenues and total expenses are equal, leading to a net income of zero.

Operating Leverage

A measure of how sensitive a company's operating income is to a change in revenue, indicating the degree to which a firm can increase operating income by increasing sales.