https://www.chenk.top/zh/tags/cramers-rule/Recent content in Cramer's Rule on Chen Kai BlogHugozh-CNWed, 22 Jan 2025 09:00:00 +0000https://www.chenk.top/zh/linear-algebra/04-%E8%A1%8C%E5%88%97%E5%BC%8F%E7%9A%84%E7%A7%98%E5%AF%86/Wed, 22 Jan 2025 09:00:00 +0000https://www.chenk.top/zh/linear-algebra/04-%E8%A1%8C%E5%88%97%E5%BC%8F%E7%9A%84%E7%A7%98%E5%AF%86/<h2 id="跳出公式行列式到底是什么" class="heading-anchor">跳出公式：行列式到底是什么<a href="#%e8%b7%b3%e5%87%ba%e5%85%ac%e5%bc%8f%e8%a1%8c%e5%88%97%e5%bc%8f%e5%88%b0%e5%ba%95%e6%98%af%e4%bb%80%e4%b9%88" class="heading-link" aria-label="Permalink to this section" title="Copy link to this section">#</a> </h2><span class="math-block">$$ \det\begin{pmatrix}a &amp; b\\ c &amp; d\end{pmatrix} = ad - bc. $$</span> <p> 记住公式，代入数字，算出结果——这种教法完全忽略了行列式的本质。</p> <p><figure class="article-figure"> <img src="https://blog-pic-ck.oss-cn-beijing.aliyuncs.com/posts/zh/linear-algebra/04-%e8%a1%8c%e5%88%97%e5%bc%8f%e7%9a%84%e7%a7%98%e5%af%86/illustration_1.png" alt="线性代数（四）：行列式的秘密 — 章节概览图" loading="lazy" decoding="async" class="content-image"> </figure> </p> <p>一句话点明核心：</p> <blockquote> <p><strong>行列式 <span class="math-inline">$\det(A)$</span> 就是变换 <span class="math-inline">$A$</span> 对面积（2D）或体积（3D）的缩放倍数。</strong></p>