Q1: What is the first step for the Gaussian elimination for the following system? $$ \left( \begin{array}{ccc|c}1 & 0 & 3 & 0 \ 2 & 1 & 1 & 0 \ 0 & 0 & 1 & 1 \ \end{array} \right) $$

A1: From the second row, we want to subtract 2 times the first row.

A2: From the first row, we want to subtract 2 times the first row.

A3: From the third row, we want to subtract 2 times the first row.

A4: From the second row, we want to subtract 2 times the third row.

A5: From the second row, we want to subtract $\frac{1}{2}$ times the first row.

Q2: What is a solution of the following system? $$ \left( \begin{array}{ccc|c}1 & 0 & 3 & 0 \ 0 & 1 & 1 & 0 \ 0 & 0 & 1 & 1 \ \end{array} \right) $$

A1: $$ \begin{pmatrix} -3 \ -1 \ 1 \end{pmatrix} $$

A2: $$ \begin{pmatrix} 3 \ 1 \ 1 \end{pmatrix} $$

A3: $$ \begin{pmatrix} 1 \ 0 \ 1 \end{pmatrix} $$

A4: $$ \begin{pmatrix} 3 \ 0 \ 1 \end{pmatrix} $$

A5: $$ \begin{pmatrix} 3 \ 0 \ -1 \end{pmatrix} $$