---
layout: doc
title: 经济数学II
breadcrumb: 经济数学II
description: 经济管理类课程《经济数学II》（线性代数）教学大纲、授课课件与复习专题讲义。内容涵盖行列式、矩阵代数与线性方程组。
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      content: 经济数学II, 线性代数, 行列式, 矩阵运算, 线性方程组, 课件下载, 复习讲义
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# 经济数学II

《经济数学II》面向经济管理类专业，授课主体内容为**线性代数**。本页面提供章节课件与复习讲义下载。

<p class="mobile-desktop-hint">建议使用电脑桌面端访问，以获得更佳的课件浏览与下载体验。</p>

---

## 章节大纲与课件下载

### 第 1 章：行列式

<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">章节</th>
      <th style="width: 73%">知识要点</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="chap-num">1.1</td>
      <td class="chap-title">行列式的定义</td>
      <td class="download-cell"><a :href="CDN_BASE + '/1-1_Determinant_Definition.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">1.2</td>
      <td class="chap-title">行列式的性质</td>
      <td class="download-cell"><a :href="CDN_BASE + '/1-2_Determinant_Properties.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">1.3</td>
      <td class="chap-title">行列式展开定理</td>
      <td class="download-cell"><a :href="CDN_BASE + '/1-3_Determinant_Expansion_Theorem.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">1.3.5</td>
      <td class="chap-title">范德蒙德行列式</td>
      <td class="download-cell"><a :href="CDN_BASE + '/1-3_5_Vandermonde_Determinant.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">1.4</td>
      <td class="chap-title">克拉默法则与矩阵概念</td>
      <td class="download-cell"><a :href="CDN_BASE + '/1-4_Cramers_Rule_and_Matrix_Concept.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr class="review-row">
      <td class="chap-num">复习</td>
      <td class="chap-title font-review">本章专题复习与行列式计算方法讲义</td>
      <td class="download-cell">
        <div class="dl-group">
          <a :href="CDN_BASE + '/handout_ch1_determinants_student.pdf'" target="_blank" rel="noopener" class="btn-dl btn-review">学生版 📂</a>
        </div>
      </td>
    </tr>
  </tbody>
</table>

### 第 2 章：矩阵及其运算

<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">章节</th>
      <th style="width: 73%">知识要点</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="chap-num">2.1</td>
      <td class="chap-title">矩阵的定义与运算</td>
      <td class="download-cell"><a :href="CDN_BASE + '/2-1_Matrix_Operations.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">2.2</td>
      <td class="chap-title">逆矩阵</td>
      <td class="download-cell"><a :href="CDN_BASE + '/2-2_Inverse_Matrix.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">2.3</td>
      <td class="chap-title">分块矩阵</td>
      <td class="download-cell"><a :href="CDN_BASE + '/2-3_Block_Matrix.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr class="review-row">
      <td class="chap-num">复习</td>
      <td class="chap-title font-review">本章专题复习与矩阵代数经典计算讲义</td>
      <td class="download-cell">
        <div class="dl-group">
          <a :href="CDN_BASE + '/handout_ch2_matrix_operations_student.pdf'" target="_blank" rel="noopener" class="btn-dl btn-review">学生版 📂</a>
        </div>
      </td>
    </tr>
  </tbody>
</table>

### 第 3 章：矩阵的初等变换与线性方程组

<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">章节</th>
      <th style="width: 73%">知识要点</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="chap-num">3.1</td>
      <td class="chap-title">矩阵的初等变换</td>
      <td class="download-cell"><a :href="CDN_BASE + '/3-1_Elementary_Transformations.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">3.2</td>
      <td class="chap-title">矩阵的秩</td>
      <td class="download-cell"><a :href="CDN_BASE + '/3-2_Matrix_Rank.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">3.3</td>
      <td class="chap-title">线性方程组消元法</td>
      <td class="download-cell"><a :href="CDN_BASE + '/3-3_Elimination_Method.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr class="review-row">
      <td class="chap-num">复习</td>
      <td class="chap-title font-review">本章专题复习与线性方程组消元求解大题讲义</td>
      <td class="download-cell">
        <div class="dl-group">
          <a :href="CDN_BASE + '/handout_ch3_elimination_systems_student.pdf'" target="_blank" rel="noopener" class="btn-dl btn-review">学生版 📂</a>
        </div>
      </td>
    </tr>
  </tbody>
</table>

::: info 线性方程组解的判定与求解流程
本图梳理通过初等行变换将增广矩阵化为行阶梯形后，如何利用系数矩阵秩 $r(A)$ 与增广矩阵秩 $r(\bar{A})$ 的关系判断解的情况，并继续求唯一解或通解。

<p align="center" style="margin: 24px 0 12px;">
  <img src="/assets/images/solution_judgment_flowchart_unified.svg" alt="线性方程组解的判定与求解流程图" style="max-width: 100%; border-radius: 12px; box-shadow: var(--shadow-sm); background: #ffffff; padding: 12px; border: 1px solid rgba(0,0,0,0.05);" />
</p>
:::

### 第 4 章：向量组的线性相关性

<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">章节</th>
      <th style="width: 73%">知识要点</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="chap-num">4.1</td>
      <td class="chap-title">向量与线性相关性</td>
      <td class="download-cell"><a :href="CDN_BASE + '/4-1_Vectors_and_Linear_Dependence.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">4.2</td>
      <td class="chap-title">向量组的秩</td>
      <td class="download-cell"><a :href="CDN_BASE + '/4-2_Rank_of_Vector_Groups.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">4.3</td>
      <td class="chap-title">线性方程组解的结构</td>
      <td class="download-cell"><a :href="CDN_BASE + '/4-3_Solution_Structure.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr class="review-row">
      <td class="chap-num">复习</td>
      <td class="chap-title font-review">本章专题复习与线性方程组解的结构讲义</td>
      <td class="download-cell">
        <div class="dl-group">
          <a :href="CDN_BASE + '/handout_ch4_vector_dependence_student.pdf'" target="_blank" rel="noopener" class="btn-dl btn-review">学生版 📂</a>
        </div>
      </td>
    </tr>
  </tbody>
</table>


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