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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 4535, 142]*) (*NotebookOutlinePosition[ 5389, 172]*) (* CellTagsIndexPosition[ 5345, 168]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[StyleBox["Preliminaries", FontFamily->"Times", FontSize->18]], "Input", TextAlignment->Center, ImageRegion->{{-0, 1}, {0, 1}}], Cell[BoxData[{ \(Author : \ Thomas\ Shores\), "\[IndentingNewLine]", \(University\ of\ Nebraska\), "\[IndentingNewLine]", \(Send\ comments\ \(to : \ tshores@math . unl . edu\)\)}], "Input", FontFamily->"Helvetica", FontWeight->"Plain", FontVariations->{"CompatibilityType"->0}], Cell[CellGroupData[{ Cell[TextData[{ "Matrix and Vector Formatting in ", StyleBox["Mathematica", FontSlant->"Italic"] }], "Subsection", ImageRegion->{{-0, 1}, {0, 1}}], Cell[TextData[{ "We are going to cover several aspects of matrices today. But first, we \ need to understand how", StyleBox[" Mathematica", FontSlant->"Italic"], " handles matrices and vectors. This preliminary material (and much more!) \ is covered in the ", StyleBox["Mathematica", FontSlant->"Italic"], " book, pages 437-460. For example, here is how we would express a \ matrix from class notes that appeared as the augmented matrix of a linear \ system. Click on the next cell and press the key." }], "Text", ImageRegion->{{-0, 1}, {0, 1}}], Cell["a = {{1,1,1,2},{2,2,4,8},{0,0,2,2}}", "Input", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ This doesn't look very much like a matrix. To pretty it up a bit, \ click on the following cell.\ \>", "Text", ImageRegion->{{-0, 1}, {0, 1}}], Cell["MatrixForm[a]", "Input", ImageRegion->{{-0, 1}, {0, 1}}], Cell[TextData[{ "Notice how a matrix consists of a list of lists (really rows), all of the \ same length. From a mathematical point of view vectors are merely special \ cases of matrices. However, ", StyleBox["Mathematica", FontSlant->"Italic"], " treats a vector as a different sort of object than a matrix. After all, \ it is rather inconvenient to define the right hand side vector b as follows: \ " }], "Text", ImageRegion->{{-0, 1}, {0, 1}}], Cell["b = {{2},{8},{2}}", "Input", ImageRegion->{{-0, 1}, {0, 1}}], Cell["MatrixForm[b]", "Input", ImageRegion->{{-0, 1}, {0, 1}}], Cell[TextData[{ "By the way, because ", StyleBox["Mathematica", FontSlant->"Italic"], " has been updated, you can click on and evaluate two cells at once (or \ drag the cursor over the right hand brackets on the cells above and hit \ )." }], "Text", ImageRegion->{{-0, 1}, {0, 1}}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " prefers to think of b as a simple list, without reference to row or \ column orientation. 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