From 182aeeddbf1a6beb7b8808c11b97502c42e59c67 Mon Sep 17 00:00:00 2001
From: idealist999 <2974730459@qq.com>
Date: Wed, 31 Dec 2025 19:15:47 +0800
Subject: [PATCH] vault backup: 2025-12-31 19:15:47

---
 .../试卷/1231线性代数考试卷（解析版）.md       | 5 ++++-
 1 file changed, 4 insertions(+), 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 59fe444..645fe8b 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
@@ -188,7 +188,6 @@ $$A^n = 6^{n-1}\begin{bmatrix}3&-1\\-9&3\end{bmatrix} $$
 ---
 
 
-
 11. 矩阵(陈峰华原创题)$$A=\begin{bmatrix}
 0 & 0 & 0 & \cdots & 0 & 1 & 1 & \cdots & 1 & 1 & 1 \\
 0 & 0 & 0 & \cdots & 0 & 0 & 1 & \cdots & 1 & 1 & 1 \\
@@ -203,6 +202,10 @@ $$A^n = 6^{n-1}\begin{bmatrix}3&-1\\-9&3\end{bmatrix} $$
 0 & 0 & 0 & \cdots & 0 & 0 & 0 & \cdots & 0 & 0 & 0 
 \end{bmatrix}_{(mn) \times (mn)}$$其中第一行有$m$个$0$.若$A^k=O$，则 $k$ 的最小值为$\underline{\qquad\qquad\qquad\qquad}.$
 
+---
+解析：
+
+
 12. 设 $A, B$ 均为 $n$ 阶方阵，满足$\text{rank} \begin{bmatrix} A \\ B \end{bmatrix} = \text{rank}B,$ 且方程 $XA = B$ 有解。若 $\operatorname{rank} A = k$，则$\text{rank} \begin{bmatrix} B & O \\ A & E \end{bmatrix} =\underline{\hspace{3cm}}.$