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<p></p>
<p align="justify">We'd like to be able to "invert <em>A</em>" to solve <em>A</em>x = b, but <em>A</em> may have only a left inverse or right inverse (or no inverse). This discussion of how and when matrices have inverses improves our understanding of the four fundamental subspaces and of many other key topics in the course.</p>
<p><em>Note: In the Fall of 1999, when the lecture videos were recorded, this lecture was given after exam 3. For the OCW Scholar version of the course we have moved it into the main body of material.</em></p>
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<h3 class="hd hd-2">Left and Right Inverses; Pseudoinverse</h3>
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<h2 class="hd hd-2 unit-title">Lecture Summary and Reading</h2>
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<h3>Lecture Summary</h3>
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<h3>Suggested Reading</h3>
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<li>Read Section 7.3 in the 4<sup>th</sup> edition or Section 8.3 in the 5<sup>th</sup> edition.</li>
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