The Augmented Matrix Is Given for a System of Equations $$\left[ \begin{array} { r r r r } 1 & 2 & - 3 & - 6 \\0 & 1 & 4 & 7 \\0 & 0 & 0 & 2\end{array} \right]$$

question 8

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.
- $$\left[ \begin{array} { r r r r } 1 & 2 & - 3 & - 6 \\0 & 1 & 4 & 7 \\0 & 0 & 0 & 2\end{array} \right]$$

• A) \(x _ { 1 } = - 20 + 11 x _ { 3 }\)
• \[\begin{array} { l }
• x _ { 2 } = 7 - 4 x _ { 3 } \\
• x _ { 3 } = 2
• \end{array}\]
• B) No solution
• C) \(x _ { 1 } = - 6 - 2 x _ { 2 } + 3 x _ { 3 }\)
• \(x _ { 2 }\) is free
• \(x _ { 3 }\) is free
• D) \(\mathrm { x } _ { 1 } = - 20 + 11 \mathrm { x } _ { 3 }\)
• \(x _ { 2 } = 7 - 4 x _ { 3 }\)
• \(x _ { 3 }\) is free

---

Definitions:

Elm Tree

A type of deciduous tree known for its broad leaves and vase-like shape, often planted in urban environments for its aesthetic value.

Neighbors

Individuals or entities that exist in close physical proximity to one another, often implying a social relationship or community connection.

Two-Paycheck

A household income scenario where two earners, typically in a family, contribute to the financial inflow.

Families

Groups of individuals related by blood, marriage, or adoption, living together or closely associated in a household.