https://www.chenk.top/zh/tags/gaussian-elimination/Recent content in Gaussian Elimination on Chen Kai BlogHugozh-CNWed, 29 Jan 2025 09:00:00 +0000https://www.chenk.top/zh/linear-algebra/05-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84%E4%B8%8E%E5%88%97%E7%A9%BA%E9%97%B4/Wed, 29 Jan 2025 09:00:00 +0000https://www.chenk.top/zh/linear-algebra/05-%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84%E4%B8%8E%E5%88%97%E7%A9%BA%E9%97%B4/<h2 id="一个贯穿始终的核心问题" class="heading-anchor">一个贯穿始终的核心问题<a href="#%e4%b8%80%e4%b8%aa%e8%b4%af%e7%a9%bf%e5%a7%8b%e7%bb%88%e7%9a%84%e6%a0%b8%e5%bf%83%e9%97%ae%e9%a2%98" class="heading-link" aria-label="Permalink to this section" title="Copy link to this section">#</a> </h2><p>在应用数学中，几乎所有问题最终都会归结为同一个核心问题：</p> <p><figure class="article-figure"> <img src="https://blog-pic-ck.oss-cn-beijing.aliyuncs.com/posts/zh/linear-algebra/05-%e7%ba%bf%e6%80%a7%e6%96%b9%e7%a8%8b%e7%bb%84%e4%b8%8e%e5%88%97%e7%a9%ba%e9%97%b4/illustration_1.png" alt="线性代数（五）：线性方程组与列空间 — 章节概览图" loading="lazy" decoding="async" class="content-image"> </figure> </p> <blockquote> <p>给定矩阵 <span class="math-inline">$A$</span> 和向量 <span class="math-inline">$\vec{b}$</span> ，方程 <span class="math-inline">$A\vec{x} = \vec{b}$</span> 是否有解？如果有，有多少个？</p> </blockquote> <p>机械式的回答是“消元后看结果”，但<strong>结构性的回答</strong>才真正有趣——这也是本章的目标。三个几何对象足以揭示一切：</p>