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

question 65

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

• A) \(( - 1,7 )\)
• B) \(x _ { 1 } = - 1 + 5 x _ { 2 }\)
• \(x _ { 2 }\) is free
• C) No solution
• D) \(x _ { 1 } = - 1 + 5 x _ { 2 }\)
• \(x _ { 2 } = 7\)
• \(x _ { 3 }\) is free

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Definitions:

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The proportion of the workforce that is unemployed and actively seeking work.

Long-run Phillips Curve

An economic concept that represents the relationship between inflation and unemployment when the effects of short-term shocks have dissipated, showing no trade-off between inflation and unemployment in the long run.

Natural Rate

A concept in economics referring to the level of unemployment at which there is no cyclical or deficient-demand unemployment. It represents a balance between the supply of labor and job vacancies, considering that some frictional and structural unemployment is inevitable.