The Augmented Matrix Is Given for a System of Equations $$\left[ \begin{array} { r r r r r } 1 & 4 & - 2 & - 3 & 1 \\0 & 0 & 1 & 4 & - 4 \\- 1 & - 4 & 0 & - 5 & 7\end{array} \right]$$

question 38

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.
- $$\left[ \begin{array} { r r r r r } 1 & 4 & - 2 & - 3 & 1 \\0 & 0 & 1 & 4 & - 4 \\- 1 & - 4 & 0 & - 5 & 7\end{array} \right]$$

• A) \(x _ { 1 } = - 4 x _ { 2 } + 2 x _ { 3 } + 3 x _ { 4 } + 1\)
• \(x _ { 2 }\) is free
• \(x _ { 3 } = - 4 - 4 x _ { 4 }\)
• \(x _ { 4 }\) is free
• B) \(\times _ { 1 } = - 7 - 4 \times _ { 2 } - 5 x _ { 4 }\)
• \(x _ { 2 }\) is free
• \(x _ { 3 } = - 4 - 4 x _ { 4 }\)
• \(x _ { 4 }\) is free
• C) \(x _ { 1 } = - 7 - 4 x _ { 2 } - 5 x _ { 4 }\)
• \(x _ { 2 }\) is free
• \(x _ { 3 } = - 4 - 4 x _ { 4 }\)
• \(x _ { 4 } = 0\)
• D) \(x _ { 1 } = - 7 - 4 x _ { 2 } - 5 \times 3\)
• \(x _ { 2 } = - 4 - 4 x _ { 3 }\)
• \(x _ { 3 }\) is free

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Definitions:

Caregivers

Individuals who provide care to those who need assistance due to various reasons, including illness, disability, or age.

Reliable

The quality of being consistently good in performance, giving the same results on successive trials, or being trustworthy.

Test Results

The outcome or findings from a series of tests or examinations, usually measuring proficiency, understanding, or condition in various contexts.

Consistent

Showing steady conformity to a standard, pattern, or expectation without any deviation or contradiction.