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\begin{center}\begin{large} Arrays and Matrices \\
\end{large} Matchett, \today
\end{center}
Arrays are produced in math mode with the \emph{array} command.
An array with 4 rows and 3 columns is produced by the following
syntax:
\begin{verbatim}
\begin{array}{***} row1 \\ row2 \\ row3 \\ row4 \end{array}
\end{verbatim}
Here each * is one of the letters, c, l, or r, and each row
consists of 3 entries separated by ampersands. Note that each
row ends with a double backslash except for the last row which
simply ends with the command that ends the environment.
Here is a comprehensive example. If you put the lines,
\begin{verbatim}
\begin{displaymath}
\begin{array}{ccr} 271 & 828 & 182 \\ 4 & 5 & 9 \\
0 & 8+x & 2 \\ 1 & 2 & 3 \end{array}
\end{displaymath}
\end{verbatim}
in a LaTeX file, the pdf file will have the display,
\begin{displaymath}
\begin{array}{ccr} 271 & 828 & 182 \\ 4 & 5 & 9 \\
0 & 8+x & 2 \\ 1 & 2 & 3 \end{array}
\end{displaymath}
Which of the three letters l, r, and c is used for a particular
column determines whether the column is left justified, right
justified, or centered.
We often want to enclose a matrix in large brackets. This is
accomplished by the commands $\backslash$left[ and $\backslash$right].
One could use parentheses, curley braces, or vertical lines as large
delimiters here instead of brackets. So the following syntax:
\begin{verbatim}
\left[ \begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array} \right)
\end{verbatim}
produces
\begin{displaymath}
\left[ \begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array} \right)
\end{displaymath}
Remember that a curley brace that is to be printed in the pdf
file must be preceeded by a backslash in the LaTeX file. LaTeX
keeps track of ``left'' and ``right'' delimiters, and requires
that they come in left-right pairs. However, as the above
example shows, a pair can be mismatched as long as there is a
left one and a right one. LaTeX treats an array as a single
large character. So arrays may be easily used in equations, like
\begin{displaymath}
A = \left[ \begin{array}{cc} 8 & 9 \\ u & v \end{array} \right]
\end{displaymath}
If it is desired to have a large delimiter on only one side of an
array, that delimiter can be paired with a period on the other
side. Here is an example of that. The latex expression,
\begin{verbatim}
f(x) = \left\{ \begin{array}{rl}
2x, & x \le 1 \\ 3-x, & x > 1
\end{array} \right.
\end{verbatim}
produces
\begin{displaymath}
f(x) = \left\{ \begin{array}{rl}
2x, & x \le 1 \\ 3-x, & x > 1
\end{array} \right.
\end{displaymath}
in the pdf file.
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