Write Y as an Affine Combination of the Other Points

question 4

Multiple Choice

Write y as an affine combination of the other points listed.
- $$\mathbf { v } _ { 1 } = \left[ \begin{array} { r } 3 \\- 2\end{array} \right] , \mathbf { v } _ { 2 } = \left[ \begin{array} { r } 1 \\- 1\end{array} \right] , \mathbf { v } _ { 3 } = \left[ \begin{array} { r } 9 \\- 1\end{array} \right] , \mathbf { y } = \left[ \begin{array} { l } 7 \\4\end{array} \right]$$

• A) \(\mathbf { y } = \mathbf { v } _ { 1 } - 2 \mathbf { v } _ { 2 } + 2 \mathbf { v } _ { 3 }\)
• B) \(\mathbf { y } = - 5 \mathbf { v } _ { 1 } + 4 \mathbf { v } _ { 2 } + 2 \mathbf { v } _ { 3 }\)
• C) \(\mathbf { y } = 4 \mathbf { v } _ { 1 } - 2 \mathbf { v } _ { 2 } - \mathbf { v } _ { 3 }\)
• D) \(\mathbf { y } = 3 \mathbf { v } _ { 1 } + 3 \mathbf { v } _ { 2 } - 5 \mathbf { v } _ { 3 }\)

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Definitions:

Overpopulation

A condition where an area's population exceeds the capacity of the environment to support it at an acceptable standard of living.

Capitalism

A financial structure where the means for producing goods and services are privately owned, aiming to generate profit.

Exurbs

Rural residential areas within commuting distance of the city.

Thomas Malthus

An English economist and demographer known for his theory on population growth and its potential impacts on resources.