The Matrix Is the Reduced Echelon Matrix for a System $$\left[ \begin{array} { r r r r | r } 1 & 0 & 0 & 10 & - 8 \\0 & 1 & 0 & 0 & 5 \\0 & 0 & 1 & 6 & 3 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

question 83

Multiple Choice

The matrix is the reduced echelon matrix for a system with variables x 1 , x 2 , x 3 , and x 4 . Find the solution set of the system. $$\left[ \begin{array} { r r r r | r } 1 & 0 & 0 & 10 & - 8 \\0 & 1 & 0 & 0 & 5 \\0 & 0 & 1 & 6 & 3 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

• A) ( \(-\) 8 \(-\) 10 k , 5, 3 \(-\) 6 k , k ), where k is any real number
• B) ( \(-\) 8 \(-\) 10 k , 5, 3 + 6 k , k ), where k is any real number
• C) ( \(-\) 8 + 10 k , 5, 3 \(-\) 6 k , k ), where k is any real number
• D) ( \(-\) 8 + 10 k , 5, 3 + 6 k , k ), where k is any real number
• E) inconsistent

---

Definitions:

Personally Distressing

Experiencing discomfort or distress on a personal level due to specific circumstances or conditions.

Helplessness

A psychological state where an individual perceives they have no control over their situation, leading to decreased motivation and ability to manage future situations.

Overwhelmed

A feeling of being excessively burdened or overloaded, either emotionally or cognitively.

Epidemiology

The branch of medicine that deals with the incidence, distribution, and possible control of diseases and other factors relating to health.