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<p>For some vectors b the equation <em>A</em>x = b has solutions and for others it does not. Some vectors <em>x</em> are solutions to the equation <em>A</em>x = 0 and some are not. To understand these equations we study the column space, nullspace, row space and left nullspace of the matrix <em>A.</em></p>
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<h3 class="hd hd-2">The Four Fundamental Subspaces</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 3.6 in the 4<sup>th</sup> edition or Section 3.5 in the 5<sup>th</sup> edition.</li>
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<h3 class="hd hd-2">Computing The Four Fundamental Subspaces</h3>
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<p>Work the problems on your own and check your answers when you're done.</p>
<p><a href="/assets/courseware/v1/76262562b21dedb90d0264b8912fde45/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.1_Exercises.pdf" target="[object Object]">Exercises on the four fundamental subspaces (PDF)</a></p>
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