2009&aring;&sup1;&acute;&aelig;•&deg;&auml;&cedil;‰

# 2009&amp;aring;&amp;sup1;&amp;acute;&amp;aelig;•&amp;deg;&...

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Unformatted text preview: 2009 年全国硕士研究生入学统一考试 数学三线性代数试题 一、 选择题：每小题 4 分 (5)设 B A , 均为 2 阶矩阵， * * . B A 分别 B A , 的伴随矩阵，若 3 , 2 = = B A 则分块矩阵 ⎜ ⎝ ⎛ B ⎟ ⎠ ⎞ A 的伴随矩阵为（ ） (A). ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 2 3 * * A B (B). ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 3 2 * * A B (C). ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 2 3 * * B A (D). ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 3 2 * * B A 【答案】(B) 【解析】由于分块矩阵 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ B A 的行列式 6 3 2 ) 1 ( 2 2 = × = − = × B A B A ，即分块 矩阵可逆，根据公式 , * 1 − = C C C ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − − ∗ 1 1 6 6 * * 1 1 1 A A B B A B B A B A B A ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ = 3 2 2 1 3 1 6 * * * * A B A B ， 故答案为（B）． 【讲评】本题考查的知识点有：伴随矩阵和 逆矩阵的关系，分块矩阵的行列式，分块矩 阵的逆矩阵等． (6)设 P A , 均为 3 阶矩阵， T P 为 P 的转置矩 阵，且 ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = 2 1 1 AP P T ，若 ) ,...
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## This note was uploaded on 12/14/2011 for the course MATH Probabilit taught by Professor Sata during the Summer '08 term at Tianjin University.

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2009&amp;aring;&amp;sup1;&amp;acute;&amp;aelig;•&amp;deg;&...

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