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

question 51

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.
- $$\left[ \begin{array} { r r r r } 1 & 0 & 6 & 3 \\0 & 1 & - 2 & - 3 \\0 & 0 & 0 & 0\end{array} \right]$$

• A) \(x _ { 1 } = 3 - 6 x _ { 3 }\)
• \(x _ { 2 } = - 3 + 2 x _ { 3 }\)
• \(x _ { 3 } = 0\)
• B) \(x _ { 1 } = 3 - 6 x _ { 3 }\)
• \(x _ { 2 }\) is free
• \(x _ { 3 } = \frac { 3 } { 2 } + \frac { 1 } { 2 } x _ { 2 }\)
• C) \(x _ { 1 } = 3 - 6 x _ { 3 }\)
• \(x _ { 2 } = - 3 + 2 x _ { 3 }\)
• \(\mathrm { x } _ { 3 }\) is free
• D) No solution

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Definitions:

Directed Remembering

Directed remembering involves consciously focusing one's effort to recall specific information or memories when prompted.

Goal-driven

Behavior or activity that is directed towards achieving specific objectives or outcomes.

Information Recall

The ability to retrieve and reproduce information from memory that was previously learned or experienced.

Analogical Inconsistency

Discrepancies or lack of uniformity in reasoning or outcomes when comparing two similar situations or analogies.