Let H Be the Hyperplane Through the Points $$\left[ \begin{array} { r } - 1 \\3\end{array} \right] , \left[ \begin{array} { r } 3 \\- 4\end{array} \right]$$

question 21

Multiple Choice

Let H be the hyperplane through the points. Find a linear functional f and a real number d such that H = [f : d].
- $$\left[ \begin{array} { r } - 1 \\3\end{array} \right] , \left[ \begin{array} { r } 3 \\- 4\end{array} \right]$$

• A) \(f \left( x _ { 1 } , x _ { 2 } \right) = - 7 x _ { 1 } + 4 x _ { 2 } , d = 19\)
• B) \(f \left( x _ { 1 } , x _ { 2 } \right) = 7 x _ { 1 } + 4 x _ { 2 } , d = 5\)
• C) \(f \left( x _ { 1 } , x _ { 2 } \right) = 3 x _ { 1 } - 4 x _ { 2 } , d = - 15\)
• D) \(f \left( x _ { 1 } , x _ { 2 } \right) = - x _ { 1 } + 3 x _ { 2 } , d = 10\)

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The revenue brought in, consistently over time, from professional endeavors or investments.

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The limits imposed on household choices by income, prices, and taxes, defining the combination of goods and services they can afford.

Income

Proceeds obtained, often periodically, from labor or investment returns.

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A measure of satisfaction or happiness that consumers derive from the consumption of goods and services.