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<h2 class="hd hd-2 unit-title">Four Fundamental Subspaces</h2>
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<p><img height="240" width="350" src="/assets/courseware/v1/7fc6946a3b01018c00c32488c100e137/asset-v1:OCW+18.06SC+2T2019+type@asset+block/Unit_1_WIDE.jpg" alt="Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang" /></p>
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<p class="caption"><span style="color: #999999;"> The big picture of linear algebra: Four Fundamental Subspaces.</span></p>
<p>Mathematics is a tool for describing the world around us. Linear equations give some of the simplest descriptions, and systems of linear equations are made by combining several descriptions.</p>
<p>In this unit we write systems of linear equations in the matrix form <em>Ax</em> = b. We explore how the properties of <em>A</em> and b determine the solutions <em>x</em> (if any exist) and pay particular attention to the solutions to <em>Ax</em> = 0. For a given matrix <em>A</em> we ask which b can be written in the form <em>Ax</em>.</p>
<p>Looking for something specific in this course? The <a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/51689f6d83d445f2b5ceea8924984b16" target="[object Object]">Resource Index</a> compiles links to most course resources in a single page. </p>
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