From 18da8b2f677bfe00525d54dca47bd1dbaf82650c Mon Sep 17 00:00:00 2001
From: Elwood <3286545699@qq.com>
Date: Fri, 2 Jan 2026 01:10:35 +0800
Subject: [PATCH 1/2] vault backup: 2026-01-02 01:10:35

---
 编写小组/试卷/1231线性代数考试卷（解析版）.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/编写小组/试卷/1231线性代数考试卷（解析版）.md b/编写小组/试卷/1231线性代数考试卷（解析版）.md
index aa594eb..f9048b1 100644
--- a/编写小组/试卷/1231线性代数考试卷（解析版）.md
+++ b/编写小组/试卷/1231线性代数考试卷（解析版）.md
@@ -45,7 +45,7 @@ tags:
 >C. $\begin{bmatrix}\alpha_1&\alpha_3&\alpha_4\end{bmatrix}=\begin{bmatrix}0&1&-1\\0&-1&1\\c_1&c_3&c_4\end{bmatrix}\cong\begin{bmatrix}0&0&-1\\0&0&1\\c_1&c_3+c_4&c_4\end{bmatrix}\cong\begin{bmatrix}0&0&0\\0&0&1\\c_1&c_3+c_4&c_4\end{bmatrix}$，故其必定线性相关；
 >D. $\begin{bmatrix}\alpha_1&\alpha_2&\alpha_4\end{bmatrix}=\begin{bmatrix}0&1&-1\\1&-1&1\\c_2&c_3&c_4\end{bmatrix}\cong\begin{bmatrix}0&0&-1\\1&0&1\\c_2&c_3+c_4&c_4\end{bmatrix}$，当$c_3+c_4\ne 0$时，作初等列变换，$\text{rank}\begin{bmatrix}0&0&-1\\1&0&1\\c_2&c_3+c_4&c_4\end{bmatrix}=\text{rank}\begin{bmatrix}0&0&1\\1&0&0\\0&1&0\end{bmatrix}=3$，故线性无关；
 
-4. 设 $A, B$ 为 $n$ 阶矩阵，则
+4. 设 $A, B$ 为 $n$ 阶矩阵，则 
    (A) $\text{rank}[A \ AB] = \text{rank} A$;  
    (B) $\text{rank}[A \ BA] = \text{rank} A$;  
    (C) $\text{rank}[A \ B] = \max\{\text{rank} A, \text{rank} B\}$;  

From 21185704ce19d0a56608945ad6cb8e039b197f1d Mon Sep 17 00:00:00 2001
From: Elwood <3286545699@qq.com>
Date: Sat, 3 Jan 2026 16:17:09 +0800
Subject: [PATCH 2/2] vault backup: 2026-01-03 16:17:09

---
 编写小组/试卷/0103高数模拟试卷（解析版）.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/编写小组/试卷/0103高数模拟试卷（解析版）.md b/编写小组/试卷/0103高数模拟试卷（解析版）.md
index 5a3ea54..2616d35 100644
--- a/编写小组/试卷/0103高数模拟试卷（解析版）.md
+++ b/编写小组/试卷/0103高数模拟试卷（解析版）.md
@@ -398,7 +398,7 @@ $$
 
 **解：**
 
-当 $x \to 0$ 时，利用等价无穷小替换和泰勒展开：
+当 $x \to 0$ 时，利用等价无穷小替换和泰勒展开：9
 
 分母：$x^3 \arcsin x \sim x^3 \cdot x = x^4$