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Mathematica is a revolutionary computer algebra system (CAS) that can be used as a numerical or symbolic calculator, a tool for graphing or as a visualization system to analyze data. One of the major strengths of Mathematica is its built in high level programming language. This provides an ideal tool for forming and testing conjectures in mathematics. In this paper, we will use Mathematica to introduce the brand new concept of fixed points of a family of matrices in linear algebra. We will also show how to use the animation and sound capabilities of Mathematica to make linear algebra come alive! In the process we will discover several conjectures and theorems.
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