docs: 修正部分 typo，添加 24-25 线代 I 历年卷答案#130
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完善19.1的证明和解答
docs: 更新19章部分缺失答案
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Pull Request Overview
This PR fixes several typos in the Linear Algebra course materials and adds answer solutions for the 2024-2025 Linear Algebra I final exam.
- Corrected mathematical notation errors (missing
\ldotsoperator and vector coordinate typo) - Added comprehensive answer solutions (308 lines) for the 2024-2025 academic year Linear Algebra I (Honors) final exam
Reviewed Changes
Copilot reviewed 4 out of 4 changed files in this pull request and generated no comments.
| File | Description |
|---|---|
| 讲义/LALU-answers.tex | Adds input directive to include the new 2024-2025 exam answer file |
| 讲义/专题/3 有限维线性空间.tex | Corrects vector a_3 fourth coordinate from 2 to -2 |
| 讲义/专题/8 相抵标准形.tex | Adds missing \ldots notation in mathematical expression for proper continuity |
| 讲义/历年卷/2024-2025-1final-answer.tex | New file containing detailed solutions for 8 problems from the 2024-2025 Linear Algebra I final exam |
Note: I identified a minor issue in the new answer file at line 66 where a + operator is missing before k_n in the mathematical expression k_1\beta+k_2 A\beta+\cdots k_n A^{n-1}\beta=0. It should be k_1\beta+k_2 A\beta+\cdots+k_n A^{n-1}\beta=0 for proper mathematical notation. However, the review system does not allow comments on new files, so this cannot be formally flagged through the comment system.
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这里在正文对应位置加个 \label，然后在这里 \autoref
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\ldots（其他地方的 \cdots 用法也都检查一下），以及这一行里面 (...) 和横行 pmatrix 混用了，统一用一种，下同
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\leq -> \leqslant，其他地方同
长度为 $n$
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