Solve the Problem $$2 x _ { 1 } - 16 x _ { 2 } + 10 x _ { 3 } = 0$$

question 4

Multiple Choice

Solve the problem.
- $$2 x _ { 1 } - 16 x _ { 2 } + 10 x _ { 3 } = 0$$

• A) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] = 8 \left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] + 5 \left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right]\) (with \(x _ { 2 } , x _ { 3 }\) free)
• B) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] = x _ { 2 } \left[ \begin{array} { l } 8 \\ 0 \\ 1 \end{array} \right] + x _ { 3 } \left[ \begin{array} { r } - 5 \\ 1 \\ 0 \end{array} \right] \quad\) (with \(x _ { 2 } , x _ { 3 }\) free)
• C) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] = x _ { 2 } \left[ \begin{array} { l } 8 \\ 1 \\ 0 \end{array} \right] + x _ { 3 } \left[ \begin{array} { r } - 5 \\ 0 \\ 1 \end{array} \right] \quad \left( \right.\) with \(x _ { 2 } , x _ { 3 }\) free)
• D) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] = x _ { 2 } \left[ \begin{array} { r } - 8 \\ 1 \\ 0 \end{array} \right] + x _ { 3 } \left[ \begin{array} { l } 5 \\ 0 \\ 1 \end{array} \right] \quad\) (with \(x _ { 2 } , x _ { 3 }\) free) Find the general solution of the simple homogeneous "system" below, which consists of a single linear equation. Give your answer as a linear combination of vectors. Let \(x _ { 2 }\) and \(x _ { 3 }\) be free variables.

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Definitions:

Mediation

A process of conflict resolution where a neutral third party assists disputing parties in reaching an agreement.

Retaining Face

The act of maintaining respect, dignity, or honor in social situations, often by avoiding embarrassment or humiliation.

Mediation

The process or intervention in a dispute or negotiation by an impartial third party to help those involved reach a settlement or understanding.

Retaining Face

The act of maintaining one's dignity, honor, and respect in the social context, often by avoiding embarrassment or admitting fault.