$x_{1}+x_{2}-3 x_{3}=3$ 1. Solve the system using Gaussian elimination: $$ \begin{array}{c} -2 x_{1}-x_{2}=-4 \ 4 x_{1}+2 x_{2}+3 x_{3}=7 \end{array} $$ 2. Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given row echelon form, shown below. Determine the value(s) of $a$, such that the system has one solution. $$ \left[\begin{array}{cccc} 1 & 2 & -3 & 4 0 & 1 & 5 & 21 0 & 0& \left(a^{2}-2 ight) & a+4 \end{array} ight] $$ 3. Suppose that an augmented matrix for a system of linear equations has been reduced by row operations to the given row echelon form, shown below. solve the system for $x_{1}, X_{2}, X_{3}$ and $x_{4}$. $\left(\begin{array}{1111|1}1 & 0& 6 & 3 & 1 1 0 & 1 & 3 & 4 & 2 110 & 0 & 1 & 1 & 3\end{array} ight]$CS.SD.101||