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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