From c9e1f14b6a1994967fa289eb6ca8b3af124edf0a Mon Sep 17 00:00:00 2001
From: idealist999 <2974730459@qq.com>
Date: Wed, 31 Dec 2025 19:26:18 +0800
Subject: [PATCH] vault backup: 2025-12-31 19:26:18

---
 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 645fe8b..26a0a51 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
@@ -203,7 +203,7 @@ $$A^n = 6^{n-1}\begin{bmatrix}3&-1\\-9&3\end{bmatrix} $$
 \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：
+解析：观察得每乘一次第一行少 $m$ 个0，故最少进行 $n$ 次即可
 
 
 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$\text{rank} \begin{bmatrix} B & O \\ A & E \end{bmatrix} =\underline{\hspace{3cm}}.$