From 4f70171fc76b0b1792a0433f1d8250e157a24dcc Mon Sep 17 00:00:00 2001
From: idealist999 <2974730459@qq.com>
Date: Wed, 31 Dec 2025 19:49:32 +0800
Subject: [PATCH] vault backup: 2025-12-31 19:49:32

---
 ...231线性代数考试卷（解析版）.md | 38 +++++++++++++++++--
 1 file changed, 35 insertions(+), 3 deletions(-)

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 e875ebf..2c4fd4a 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
@@ -194,10 +194,42 @@ $$A \to \begin{bmatrix} 1 & 1 & 3 & 1 & 0 & 1 \\ 0 & 1 & 1 & -1 & 1 & 2 \\ 0 & 2
     \underline{\qquad\qquad\qquad\qquad}.
     $$
 ---
-解析：
 
-一眼顶针，鉴定为：   $$
-   x = (1,0,0,0)^T$$
+**答**：$(1,0,0,0)^T$。
+
+**解析**：由范德蒙行列式的性质可知 $|A| \neq 0$，从而线性方程组 $Ax = b$ 有唯一解。
+
+又由
+$$
+\begin{bmatrix}
+1 & a_1 & a_1^2 & a_1^3 \\
+1 & a_2 & a_2^2 & a_2^3 \\
+1 & a_3 & a_3^2 & a_3^3 \\
+1 & a_4 & a_4^2 & a_4^3
+\end{bmatrix}
+\begin{bmatrix}
+1 \\
+0 \\
+0 \\
+0
+\end{bmatrix}
+=
+\begin{bmatrix}
+1 \\
+1 \\
+1 \\
+1
+\end{bmatrix}
+$$
+可知 $Ax = b$ 的解为
+$$
+\begin{bmatrix}
+1 \\
+0 \\
+0 \\
+0
+\end{bmatrix}
+$$
 ---