$$ \left[\begin{array}{rrr|r}2 & 1 & -3 & 2 \ 2 & -3 & 1 & 10 \ -2 & 1 & 1 & -6\end{array} ight] $$ Use the following steps to reduce the augmented matrix to generalized row echelon form: Step 1: $$ R_{3}+R_{1} \longrightarrow R_{3} $$ $$ R_{2}-R_{1} \longrightarrow R_{2} $$ Step $$ 2: $$ $$ \left(-\frac{1}{4} ight) R_{2} \longrightarrow R_{2} $$ $$ \left(-\frac{1}{2} ight) R_{3} \longrightarrow R_{3} $$ Step $$ 3: $$ $$ R_{3}+R_{2} \longrightarrow R_{3} $$ Deduce that the solutions are:

Question

$$ \left[\begin{array}{rrr|r}2 & 1 & -3 & 2 \ 2 & -3 & 1 & 10 \ -2 & 1 & 1 & -6\end{array}ight] $$ Use the following steps to reduce the augmented matrix to generalized row echelon form: Step 1: $$ R_{3}+R_{1} \longrightarrow R_{3} $$ $$ R_{2}-R_{1} \longrightarrow R_{2} $$ Step $$ 2: $$ $$ \left(-\frac{1}{4}ight) R_{2} \longrightarrow R_{2} $$ $$ \left(-\frac{1}{2}ight) R_{3} \longrightarrow R_{3} $$ Step $$ 3: $$ $$ R_{3}+R_{2} \longrightarrow R_{3} $$ Deduce that the solutions are:

Mejia Ford · Accepted Answer

The solutions are $$ x = t + 2, y = t - 2, z = t $$, where $$ t $$ is a free variable.

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