2009年数一

2009å¹´æ•°&...

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Unformatted text preview: 2009 年全国硕士研究生入学统一考试 数学一线性代数试题 一、 选择题:每小题 4 分. (5)设 是 3 维向量空间 的一组 基,则由基 3 2 , 1 , a a a 3 R 3 2 1 3 1 , 2 1 , a a a 到基 1 3 3 2 2 1 , , a a a a a a + + + 的过渡矩阵为( ) (A) ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ 3 3 2 2 1 1 (B) ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ 3 1 3 2 2 1 (C) ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ − − − 6 1 4 1 2 1 6 1 4 1 2 1 6 1 4 1 2 1 ⎜ (D) ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ − − − 6 1 6 1 6 1 4 1 4 1 4 1 2 1 2 1 2 1 【答案】(A) 【解析】由基 3 2 1 3 1 , 2 1 , a a a 到 1 3 3 2 2 1 , , a a a a a a + + + 的过渡矩阵满足 ( ) ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = + + + 3 3 2 2 1 1 3 1 , 2 1 , , , 3 2 1 1 3 3 2 2 1 a a a a a a a a a 所以选(A). 【讲评】本题考查的知识点为过渡矩阵. (6)设 B A , 均为 2 阶矩阵, ∗ ∗ B A , 分别为 B A , 的伴随矩阵,若 , 3 , 2 = = B A 则分块 矩阵 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ B A O 的伴随矩阵为( ) (A) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∗ ∗ O A B O 2 3 (B) ⎟ ⎟ ⎠...
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2009å¹´æ•°&...

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