%% Created by Maple 9.50 (IBM INTEL NT)
%% Source Worksheet: UeA14_3.mws
%% Generated: Mon Jan 21 15:36:18 2013
\documentclass{article}
\usepackage{maple2e}
 \def\emptyline{\vspace{12pt}}
\DefineParaStyle{Maple Output}
\DefineCharStyle{2D Math}
\DefineCharStyle{2D Output}
\begin{document}
\pagestyle{empty}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{with(linalg):A := matrix([[3, 2, 0], [2, 4, 2], [0, 2, 5]]);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{A := matrix([[3, 2, 0], [2, 4, 2], [0, 2, 5]]);}{%
\[
A :=  \left[ 
{\begin{array}{rrr}
3 & 2 & 0 \\
2 & 4 & 2 \\
0 & 2 & 5
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{eigenvects(A);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{[1, 1, \{vector([2, -2, 1])\}], [4, 1, \{vector([2, 1, -2])\}], [7,
1, \{vector([1, 2, 2])\}];}{%
\[
[1, \,1, \,\{[2, \,-2, \,1]\}], \,[4, \,1, \,\{[2, \,1, \,-2]\}]
, \,[7, \,1, \,\{[1, \,2, \,2]\}]
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{T:=linalg[matrix](3,3,[2,2,1,-2,1,2,1,-2,2]);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{T := matrix([[2, 2, 1], [-2, 1, 2], [1, -2, 2]]);}{%
\[
T :=  \left[ 
{\begin{array}{rrr}
2 & 2 & 1 \\
-2 & 1 & 2 \\
1 & -2 & 2
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{T1:=inverse(T);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{T1 := matrix([[2/9, -2/9, 1/9], [2/9, 1/9, -2/9], [1/9, 2/9,
2/9]]);}{%
\[
\mathit{T1} :=  \left[ 
{\begin{array}{ccc}
{\displaystyle \frac {2}{9}}  & {\displaystyle \frac {-2}{9}}  & 
{\displaystyle \frac {1}{9}}  \\ [2ex]
{\displaystyle \frac {2}{9}}  & {\displaystyle \frac {1}{9}}  & 
{\displaystyle \frac {-2}{9}}  \\ [2ex]
{\displaystyle \frac {1}{9}}  & {\displaystyle \frac {2}{9}}  & 
{\displaystyle \frac {2}{9}} 
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{det(T);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{27;}{%
\[
27
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\end{mapleinput}

\emptyline
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{multiply(A,T);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{matrix([[2, 8, 7], [-2, 4, 14], [1, -8, 14]]);}{%
\[
 \left[ 
{\begin{array}{rrr}
2 & 8 & 7 \\
-2 & 4 & 14 \\
1 & -8 & 14
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{multiply(T1,A,T);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{matrix([[1, 0, 0], [0, 4, 0], [0, 0, 7]]);}{%
\[
 \left[ 
{\begin{array}{rrr}
1 & 0 & 0 \\
0 & 4 & 0 \\
0 & 0 & 7
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\end{mapleinput}

\end{maplegroup}
\end{document}
%% End of Maple 9.50 Output
