RREF.sagews

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<h2 class="heading">
<span class="title">Sage and Linear Algebra Worksheet:</span> <span class="subtitle">FCLA Section RREF</span>
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<div class="author">
<div class="author-name">Robert Beezer</div>
<div class="author-info">Department of Mathematics and Computer Science<br>University of Puget Sound</div>
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<div class="date">Fall 2019</div>
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<div class="mathbook-content"><p id="p-1">To specify a matrix, first specify that your entries are rational numbers, <code class="code-inline tex2jax_ignore">QQ</code> in Sage parlance.  This is extremely important, though an explanation is best saved for later.  Then the number of rows and columns.  Follow this with a list of rows for the matrix, where each row is another list.  We use square brackets, <code class="code-inline tex2jax_ignore">[, ]</code> to organize lists.  To actually see <code class="code-inline tex2jax_ignore">A</code> we just write it as the last line.</p></div>

A = matrix(QQ, 3, 4, [[-1,  1,  1,  1],
                      [ 2, -1, -2, -3],
                      [-2,  2,  1, -1]])
A

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<div class="mathbook-content"><p id="p-2">Then use the <code class="code-inline tex2jax_ignore">.rref()</code> method to compute the reduced row-echelon form.</p></div>

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<div class="mathbook-content"><article class="exercise-like" id="exercise-1"><h6 class="heading">
<span class="type">Demonstration</span> <span class="codenumber">1</span>.</h6>
<p id="p-3">Use a new cell, enter <code class="code-inline tex2jax_ignore">A.rref()</code>, and execute the cell.</p></article></div>

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<div class="mathbook-content"><p id="p-4">Here is a larger example.</p></div>

B = matrix(QQ, [[ 0,  0, -1,  3,  3, -1,  2, -1],
                [ 1, -5,  0, -4,  5, -2,  4,  4],
                [-1,  5, -1,  7, -2,  2, -5, -7],
                [-1,  5,  1,  1, -8,  3, -6, -3]])
B

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<div class="mathbook-content"><article class="exercise-like" id="exercise-2"><h6 class="heading">
<span class="type">Demonstration</span> <span class="codenumber">2</span>.</h6>
<p id="p-5">As above, use a new cell to compute the reduced row-echelon form of <code class="code-inline tex2jax_ignore">B</code>.</p></article></div>

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<div class="mathbook-content"><p id="p-6">This work is Copyright 2016–2019 by Robert A. Beezer.  It is licensed under a <a class="external" href="https://creativecommons.org/licenses/by-sa/4.0/" target="_blank">Creative Commons Attribution-ShareAlike 4.0 International License</a>.</p></div>

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