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<p>Now we start to use the determinant. Understanding the cofactor formula allows us to show that <em>A</em><sup>-1</sup> = (1/det<em>A</em>)<em>C<sup>T</sup></em>, where <em>C </em> is the matrix of cofactors of <em>A</em>. Combining this formula with the equation x = A<sup>-1</sup>b gives us Cramer's rule for solving <em>A</em>x = b. Also, the absolute value of the determinant gives the volume of a box.</p>
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<li>Read Section 5.3 in the 4<sup>th</sup> or 5<sup>th</sup> edition.</li>
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<p><a href="/assets/courseware/v1/22fa2a997b1cf58f9ebf067e28334e7a/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18_06_Unit_II_2.7_ChineseTrans.pdf" target="[object Object]">Recitation video transcript in Chinese (PDF)</a></p>
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<h2 class="hd hd-2 unit-title">Problems and Solutions</h2>
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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/c92f0f4955a04d45a2dd4b65ca3024ff/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.7_Exercises.pdf" target="[object Object]">Exercises on Cramer's Rule, inverse matrix, and volume (PDF)</a></p>
<p><a href="/assets/courseware/v1/eb90fd1ec1081b4f0e8aa00b55a8978c/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.7_Solutions.pdf" target="[object Object]">Solutions to Cramer's Rule, inverse matrix, and volume (PDF)</a></p>
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