The Augmented Matrix Is Given for a System of Equations $$\left[ \begin{array} { r r r r } 1 & 2 & - 3 & - 6 \\0 & 1 & 4 & 7 \\0 & 0 & 0 & 2\end{array} \right]$$

question 8

Multiple Choice

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.
Otherwise state that there is no solution.
- $$\left[ \begin{array} { r r r r } 1 & 2 & - 3 & - 6 \\0 & 1 & 4 & 7 \\0 & 0 & 0 & 2\end{array} \right]$$

• A) \(x _ { 1 } = - 20 + 11 x _ { 3 }\)
• \[\begin{array} { l }
• x _ { 2 } = 7 - 4 x _ { 3 } \\
• x _ { 3 } = 2
• \end{array}\]
• B) No solution
• C) \(x _ { 1 } = - 6 - 2 x _ { 2 } + 3 x _ { 3 }\)
• \(x _ { 2 }\) is free
• \(x _ { 3 }\) is free
• D) \(\mathrm { x } _ { 1 } = - 20 + 11 \mathrm { x } _ { 3 }\)
• \(x _ { 2 } = 7 - 4 x _ { 3 }\)
• \(x _ { 3 }\) is free

Discern the differences between majority voting outcomes and efficient resource allocation.

Understand the principles of the median-voter model and its application in predicting policy outcomes.

Evaluate the effects of political techniques like vote trading (logrolling) on economic efficiency and policy decisions.

Understand the concept of personal and social identities and their contributing factors.

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Definitions:

Nonserious Interference

Minimal or insignificant disruption that does not constitute a legal nuisance or cause substantial harm to another's property rights.

Conversion

Conversion, in legal terms, refers to an act of wrongfully taking, using, or retaining possession of personal property belonging to another without permission.

Real Property

Land and anything permanently attached to it, such as buildings and other structures.

Personal Property

Movable property that is not classified as real estate, including tangible items like cars and furniture, and intangible items such as stocks and bonds.