The Augmented Matrix Is Given for a System of Equations $$\left[ \begin{array} { r r r r r r } 1 & 5 & 8 & - 1 & 2 & 5 \\0 & 0 & 0 & - 4 & 3 & 4 \\0 & 0 & 0 & 0 & - 2 & 8\end{array} \right]$$

question 74

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.
- $$\left[ \begin{array} { r r r r r r } 1 & 5 & 8 & - 1 & 2 & 5 \\0 & 0 & 0 & - 4 & 3 & 4 \\0 & 0 & 0 & 0 & - 2 & 8\end{array} \right]$$

• A) \(x _ { 1 } = - 5 x _ { 2 } - 8 x _ { 3 } + 9\)
• \(x _ { 2 }\) is free
• \(x _ { 3 } = - 4\)
• \(x _ { 4 } = \frac { 3 } { 4 } x _ { 5 } - 1\)
• \[x _ { 5 } = - 4\]
• B) No solution
• C) \(x _ { 1 } = - 5 x _ { 2 } - 8 x _ { 3 } + x _ { 4 } - 2 x _ { 5 } + 5\)
• \(x _ { 2 }\) is free
• \(x _ { 3 }\) is free
• \[x _ { 4 } = \frac { 3 } { 4 } x _ { 5 } - 1\]
• \(x _ { 5 } = - 4\)
• D) \(x _ { 1 } = - 5 x _ { 2 } - 8 x _ { 3 } + 9\)
• \(x _ { 2 }\) is free
• \(x _ { 3 }\) is free
• \(x _ { 4 } = - 4\)
• \(x _ { 5 } = - 4\)

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Definitions:

Helplessness Stage

A psychological condition where an individual feels powerless to effect change or avoid negative situations, often a result of repeated failures or a sense of loss of control.

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Neutral Zone is a term in transition management describing the state of ambiguity and disorientation between an old reality and a new beginning.

Neutral Zone

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A situation where an individual experiences the removal or absence of something or someone valuable in their life.