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%TCIDATA{<META NAME="Title" CONTENT="Matrix Operations">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Mar 27 14:44:28 1997}
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\input{tcilatex}
\begin{document}


\subsection{Matrix Operations\label{Matrix Operations}\hrulefill}

You can perform a full range of matrix operations including addition,
multiplication, transposition, and inversion. These are just a few examples
of matrix operations:

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Transpose $%
\left[ 
\begin{array}{ll}
1 & 4 \\ 
2 & 5 \\ 
3 & 6
\end{array}
\right] $}

\begin{enumerate}
\item  Click\FRAME{itbpF}{20.125pt}{18.9375pt}{3.25pt}{}{}{sqbrack.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 20.125pt;height 18.9375pt;depth
3.25pt;original-width 20.3125pt;original-height 18.8125pt;cropleft
"0";croptop "1.0079";cropright "1";cropbottom "0";filename
'Sqbrack.wmf';file-properties "XNPEU";}}, and then from the Insert menu,
choose Matrix and specify 3 rows and 2 columns.

\item  Type \textbf{1}, press Tab, type \textbf{4}, and press Tab.

\item  Type \textbf{2}, press Tab, type \textbf{5}, and press Tab.

\item  Type \textbf{3}, press Tab, and type \textbf{6}.

\item  From the Maple menu, choose Matrices and then choose Transpose. Maple
transposes the matrix: \medskip 
\[
\fbox{$
\begin{tabular}{llll}
\rule[-0.25in]{0in}{0.6in} &  & $\left[ 
\begin{array}{ll}
1 & 4 \\ 
2 & 5 \\ 
3 & 6
\end{array}
\right] $, transpose: $\left[ 
\begin{array}{ccc}
1 & 2 & 3 \\ 
4 & 5 & 6
\end{array}
\right] $ & \rule[-0.25in]{0in}{0.6in}\ \ \ 
\end{tabular}
$}
\]
\medskip 
\end{enumerate}

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Invert $%
\left[ 
\begin{array}{cc}
1 & 2 \\ 
7 & -3
\end{array}
\right] $}

\begin{enumerate}
\item  Click\FRAME{itbpF}{20.125pt}{18.9375pt}{3.25pt}{}{}{sqbrack.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 20.125pt;height 18.9375pt;depth
3.25pt;original-width 20.3125pt;original-height 18.8125pt;cropleft
"0";croptop "1.0079";cropright "1";cropbottom "0";filename
'Sqbrack.wmf';file-properties "XNPEU";}}, and then from the Insert menu,
choose Matrix and specify 2 rows and 2 columns.

\item  Type \textbf{1}, press Tab, type \textbf{2}, press Tab, type \textbf{7%
}, press Tab,\ and type \textbf{-3}.

\item  From the Maple menu, choose Matrices and then choose Inverse. Maple
inverts the matrix: \medskip 
\[
\fbox{$
\begin{tabular}{lllll}
\rule[-0.25in]{0in}{0.6in} &  & $\left[ 
\begin{array}{cc}
1 & 2 \\ 
7 & -3
\end{array}
\right] $, inverse: $\left[ 
\begin{array}{cc}
\frac{3}{17} & \frac{2}{17} \\ 
\frac{7}{17} & -\frac{1}{17}
\end{array}
\right] $ & \rule[-0.25in]{0in}{0.6in} & 
\end{tabular}
$}
\]
\medskip 
\end{enumerate}

\subparagraph{Perform these matrix operations\protect\medskip \textit{\label%
{exercises}}}

\begin{quotation}
\[
\text{Adjugate }\left[ 
\begin{array}{ll}
97 & 50 \\ 
56 & 49
\end{array}
\right] \medskip .\text{\qquad \qquad Concatenate }\left[ 
\begin{array}{ll}
a & 5 \\ 
6 & b
\end{array}
\right] \left[ 
\begin{array}{ll}
9 & c \\ 
d & 4
\end{array}
\right] \medskip . 
\]

\[
\text{Find the determinant of }\left[ 
\begin{array}{ll}
a & b \\ 
c & d
\end{array}
\right] . 
\]
\end{quotation}

\end{document}
