Use the Gaussian Algorithm and complete the steps below to solve the following for $$

$.$

$3212321250139314=0101$

Enter the augmented matrix that results after following steps $1-4$ of the Gaussian Algorithm in structions $($p$11$ of $1\mathrm{.}2$ in the textbook$).$ You should have a leading $1$ in the first row and all entries below it equal to $0.$

Answer for part Gap $0$

Continue the steps on the next available column and enter the resulting matrix below $($remember there should be a leading $1$ in the second row with all entries below it equal to $0).$

Answer for part Gap $1$

Enter the final row$-$echelon augmented matrix

Answer for part Gap $2$

Now use this matrix to find a vector $$

that solves the system. If you have a free variable, set it to zero $($e$.$g$.,$ if $3$

is a free variable, then let $3=0$

$,$ and determine the remaining values based on that.

$=$

Answer for part Gap $3$