2-1.1(一阶、二阶和三阶行列式)

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1、第二章行列式§2.1n阶行列式的定义一.一阶、二阶和三阶行列式二.n阶行列式的定义三.定义计算简单的行列式电子科技大学黄廷祝§2.1n阶行列式的定义一.一阶、二阶和三阶行列式AXbnnb1n1ax11ba1(110)xa11baab122122xaxaxb11111221aa1122aa1221n2(aaaa0)axaxb11221221abba2112222x1121212aa1122a1221aaxaxaxb1111221331n3ax

2、axaxb2112222332axaxaxb3113223333baaaabababaaabaaab122331223313232123321223313223x1aaaaaaaaaaaaaaaaaa112233122331132132112332122133132231§2.1n阶行列式的定义AXbnnb1

3、A

4、

5、a

6、an1x一阶行列式1111a11如:行列式55，33baab122122x1aa1122aa1221aa1112n2二阶

7、行列式

8、

9、Aaaaaabbaaa11221221x11212121222aa1122a1221a21如:63333baaaabababaaabaaab122331223313232123321223313223n3x1aaaaaaaaaaaaaaaaaa112233122331132132112332122133132231aaa111213aaaaaaaaa112233122331132132三阶行列式

10、

11、Aaaa212223aaaaaaa

12、aa112332122133132231aaa313233§2.1n阶行列式的定义三阶行列式的记忆法(对角线法)aaa111213Aa21a22a23aaa112233aaa122331aaa132132aaa313233aaa132231aaa122133aaa11233212-4例1.计算三阶行列式D-221-34-2解D12(2)21(3)(4)(2)4(4)2(3)2(2)(2)11414§2.1n阶行列式的定义111例2.求解方程

13、23x0.249x解方程左端222D3x4x189x2x12x5x6,2由解得xx560x2或x3.[结束]§2.1n阶行列式的定义