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Cell[TextData[{
  "Working with matrices in ",
  StyleBox["Mathematica",
    FontSlant->"Italic"]
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Cell["\<\
Created by Professor Caleb Shor at Bates College for Math 205, Linear \
Algebra, Winter 2006.  Feel free to use this and modify as appropriate.\
\>", "Subsubsection"],

Cell[TextData[{
  "This document (called a \"notebook\" in ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " lingo) will serve as a brief introduction to working with matrices in ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  "."
}], "Text"],

Cell[TextData[{
  "We can use ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " just like a calculator.  To execute a command, hold down shift and press \
enter.  (If you just press enter, ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " thinks that you are typing a command that requires more than one line..)"
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Cell[BoxData[
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Cell[TextData[{
  StyleBox["(Mathematica",
    FontSlant->"Italic"],
  " keeps track of inputs and outputs so that we can refer back to a \
calculation if we want.)  The command '%' gives the previous output, and '%n' \
gives output number n."
}], "Text"],

Cell[BoxData[
    \(%\)], "Input"],

Cell[BoxData[
    \(%1 + %2\)], "Input"],

Cell["We can create variables and assign values to them", "Text"],

Cell[BoxData[
    \(x = 5\)], "Input"],

Cell[BoxData[
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Cell[BoxData[
    \(x^200\)], "Input"],

Cell["\<\
Lists are made with curly brackets.  We can think of a vector as a list..\
\>", "Text"],

Cell[BoxData[
    \(u = {1, 2}\)], "Input"],

Cell[BoxData[
    \(v = {1, 3}\)], "Input"],

Cell[BoxData[
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Cell["\<\
...and think of a matrix as a list of lists, where each list corresponds to a \
row of the matrix.\
\>", "Text"],

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Cell[BoxData[
    \(M = {{1, 4}, {5, \(-1\)}}\)], "Input"],

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Cell["\<\
For displaying purposes, we have the command MatrixForm, which allows us to \
see our vectors and matrices more easily.  (Arguments for commands go inside \
square brackets.)\
\>", "Text"],

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Cell["\<\
We use period \".\" to multiply a matrix with a matrix or a matrix with a \
vector.\
\>", "Text"],

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Cell[BoxData[
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Cell["\<\
If we want to use the last output in a calculation, we \"%\".  To use a \
particular output, try \"%n\", where n is the output number.\
\>", "Text"],

Cell[BoxData[
    \(MatrixForm[%]\)], "Input"],

Cell["\<\
To raise a matrix to a power, we have a special command.  Notice that \"A^2\" \
doesn't give you the same thing as \"A.A\"..\
\>", "Text"],

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Cell["\<\
A^2 has the effect of squaring each entry in the matrix, which isn't what we \
want.  To raise a matrix A to a power n, we can use the command \
MatrixPower[A,n].\
\>", "Text"],

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Cell[TextData[{
  "We can use ",
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    FontSlant->"Italic"],
  " to calculate determinants."
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Cell[TextData[{
  "Since the determinant of A is non-zero, it is invertible.  We can make an \
augmented matrix with the identity matrix and row reduce [A I] to get [I B], \
where B is the inverse of A.  (To do this, we need to load a special package \
for ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  ".)"
}], "Text"],

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Cell[TextData[{
  "Or we could have just asked ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " for the inverse to begin with.."
}], "Text"],

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Cell[TextData[{
  "There are many more things that ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " can do.  For help with specific commands, check the help browser, which \
is under the Help menu."
}], "Text"],

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  "One thing to note is that ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " will keep track of all variables that have been assigned unless you \
\"quit the kernel\", which you can do in the Kernel menu.  (When you quit ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  ", you automatically quit the kernel.)  This is something to beware of if \
you are working with multiple ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " notebooks at the same time.."
}], "Text"]
}, Open  ]],

Cell["\<\
Your first homework assignment, due on Friday, February 17, is available on \
our course webpage.  (http://www.bates.edu/~cshor/winter2006/ma205)\
\>", "Subsubsection"]
}, Open  ]]
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End of Mathematica Notebook file.
*******************************************************************)