第1章行列式

第1章行列式

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Unformatted text preview: 2008 春季班 线性代数 第 1 章 行列式 1 — 1 第 1 章 行列式 1.1 行列式的概念 n 阶行列式是一个数,是由 个数排成 行 列 的方阵 2 n n n nn n n n n a a a a a a a a a " " " " " " " 2 1 2 22 21 1 12 11 所决定的. 例如:二阶行列式 2 3 2 4 1 4 3 2 1 − = × − × = 二阶行列式一般的计算公式是 21 12 22 11 22 21 12 11 a a a a a a a a × − × = . 三阶行列式的计算公式是 33 32 31 23 22 21 13 12 11 a a a a a a a a a 2008 春季班 线性代数 第 1 章 行列式 1 — 2 32 31 22 21 13 33 31 23 21 12 33 32 23 22 11 a a a a a a a a a a a a a a a × + × − × = . 在 阶行列式中,去掉元素 所在的第 n ij a i 行和第 j 列,剩下的是一个 1 − n 阶行列式,叫做 的余子 式,记作 ij a ij M . 13 13 12 12 11 11 33 32 31 23 22 21 13 12 11 M a M a M a a a a a a a a a a + − = 记 ij j i ij M A + − = ) 1 ( 称 ij A 为 的代数余子式. ij a 13 13 12 12 11 11 33 32 31 23 22 21 13 12 11 A a A a A a a a a a a a a a a + + = . n n nn n n n n A a A a A a a a a a a a a a a 1 1 12 12 11 11 2 1 2 22 21 1 12 11 + + + = " " " " " " " " 2008 春季班 线性代数 第 1 章 行列式 1 — 3 例 1 x x x x x x x x − = − = = 2 ) 1 ( 1 1 1 1 1 1 1 . 例 2 ! 3 2 1 2 1 n n n = = × = " " " " " " " " " " " " " " " 例 3 nn nn n nn n n a a a a a a a a a a a a a " " " " " " " " " " " " " " 22 11 2 22 11 2 1 22 21 11 = = = . 2008...
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第1章行列式

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