\documentclass[a4paper,12pt]{article}
\newcommand{\ds}{\displaystyle}
\newcommand{\pl}{\partial}
\parindent=0pt
\begin{document}


{\bf Question}

Find the solutions for the following systems of equations.

\begin{description}
\item[(i)] $\ds \left( \begin{array}{ccc}2 & 4 & 1 \\ 1 & 1 & 1 \\ 2 & 3 & 1
 \end{array} \right)
\left( \begin{array}{c} x_1 \\ x_2 \\ x_3 \end{array} \right) =
\left(
\begin{array}{c} 5 \\ 6 \\ 6\end{array} \right)$
\item[(ii)]$\ds \left( \begin{array}{ccc} 5 & 15 & -10 \\ -2 & -2 & -4 \\ 3 & 4 & 1
\end{array} \right)
\left( \begin{array}{c} x_1 \\ x_2 \\ x_3 \end{array} \right) =
\left( \begin{array}{c} 0 \\ 4 \\ -5 \end{array} \right)$
\item[(iii)]$\ds \left( \begin{array}{cccc} 1 & -2 & 1 & -5 \\ 3 & -6 & 4 & -14 \\
-2 & 4 & -4 & 9 \\ 4 & -7 & 5 & -18 \end{array} \right) \left(
\begin{array}{c} x_ 1 \\ x_2 \\ x_3 \\x_4 \end{array} \right) = \left(
\begin{array}{c} 0 \\ 4 \\ 5 \\ 6\end{array} \right)$
\item[(iv)]$\ds \left( \begin{array}{ccc} 2 & 1 & -1 \\ 1 & -2 & 1 \\ 4 & -3 & 1
\end{array} \right)
\left( \begin{array}{c}x_1 \\ x_2 \\ x_3 \end{array} \right) =
\left(
\begin{array}{c} 1 \\ 3 \\ 5\end{array} \right)$
\item[(v)]$\ds \left( \begin{array}{ccc} 2 & -1 & 3 \\ 1 & 1 & -3 \\ 5 & -1 & 3
\end{array} \right)
\left( \begin{array}{c} x_1 \\ x_2 \\ x_3 \end{array} \right) =
\left(
\begin{array}{c} 4 \\ -1 \\ 7 \end{array} \right)$
\item[(vi)]$\ds \left( \begin{array}{ccc} 5 & -2 & 7 \\ -3 & 5 & -1 \\ 1 & 1 & -3
 \end{array} \right)
\left( \begin{array}{c} x_1 \\ x_2 \\ x_3 \end{array} \right) =
\left(
\begin{array}{c} 0 \\ 0 \\ 0 \end{array} \right)$
\item[(vii)] $\left(\begin{array}{cccc} 1 & -2 & 3 & -4 \\ 2 & 1 &
-1 & 1 \\ 3 & -1 & 2 & -1 \end{array} \right)\left(
\begin{array}{c} x_ 1
\\ x_2 \\ x_3 \\x_4 \end{array} \right) = \left(
\begin{array}{c} 0 \\ 0 \\ 0\end{array} \right)$
\end{description}

\vspace{.25in}

{\bf Answer}

Solutions
\begin{description}
\item[(i)] $\left( \begin{array}{c} 2\\ -1 \\ 5 \end{array} \right)$
\item[(ii)] $\left( \begin{array}{c} -3 \\1\\0\end{array} \right)$
\item[(iii)] $\left( \begin{array}{c} 52\\-11\\-9\\13\end{array} \right)$
\item[(iv)] no solutions
\item[(v)] $\left( \begin{array}{c} 1\\3t-1\\t\end{array} \right)$
\item[(vi)] $\left( \begin{array}{c} 0\\0\\0\end{array} \right)$
\item[(vii)] $\left( \begin{array}{c} -t\\7t\\5t\\0\end{array} \right)$

\end{description}


\end{document}
