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<p>Vectors are easier to understand when they're described in terms of orthogonal bases. In addition, the Four Fundamental Subspaces are orthogonal to each other in pairs.</p>
<p>If <em>A</em> is a rectangular matrix, <em>A</em>x = b is often unsolvable. The matrix <em>A</em> <sup> T </sup> <em>A</em> will help us find a vector x̂ that comes as close as possible to solving <em> A</em>x = b.</p>
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<h3 class="hd hd-2">Orthogonal Vectors and 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 4.1 in the 4<sup>th</sup> or 5<sup>th</sup> edition.</li>
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<p>Work the problems on your own and check your answers when you're done.</p>
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