Suppose that the augmented matrix of a system of linear equations for unknowns $$ x, y $$, and $$ z $$ is $$ \left[\begin{array}{ccc:c}1 & -\frac{7}{2} & \frac{11}{4} & -6 \ 5 & -\frac{35}{2} & \frac{55}{4} & -30 \ -4 & 14 & -11 & 24\end{array} ight] $$ Solve the system and provide the information requested.

Question

Suppose that the augmented matrix of a system of linear equations for unknowns $$ x, y $$, and $$ z $$ is $$ \left[\begin{array}{ccc:c}1 & -\frac{7}{2} & \frac{11}{4} & -6 \ 5 & -\frac{35}{2} & \frac{55}{4} & -30 \ -4 & 14 & -11 & 24\end{array}ight] $$ Solve the system and provide the information requested.

Cummings Norton · Accepted Answer

The system has infinitely many solutions and can be expressed as $$ x = -6 + \frac{7}{2}s - \frac{11}{4}t $$, $$ y = s $$, and $$ z = t $$, where $$ s $$ and $$ t $$ are free parameters.

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