(後只人季 1.1二阶、三阶行列式
1.1 二阶、三阶行列式
(後只人季 用消元法解二元线性方程组 12~2 dotx f goox 21 22~2 =b2.(2) (1) X (a: a 11221 十 122x2 b,a 22 (2)×a2:a242x1+(a122x 12 两式相减消去x2,得 (a12-a122)x1=ba2-a12b2;
用消元法解二元线性方程组 + = + = . , 2 1 1 2 2 2 2 1 1 1 1 2 2 1 a x a x b a x a x b (1) (2) (1) : a22 a1 1a2 2x1 + a1 2a2 2x2 = b1 a2 2, (2) : a12 a1 2a2 1x1 + a1 2a2 2x2 = b2 a1 2, 两式相减消去 x2 ,得 (1.1) (a1 1a2 2 − a1 2a2 1)x1 = b1 a2 2 − a1 2b2 ;
(後只人季 类似地,消去x,得 1122 22 112 21 当a1a2-a1221≠0时,方程的解为 b2-b1a21 l22-a 1221 1122 1221
类似地,消去x1,得 (a1 1a2 2 − a1 2a2 1)x2 = a1 1b2 − b1 a2 1, 当 α1 1α2 2 − α1 2α2 1 0 时,方程的解为 , 11 22 12 21 1 22 12 2 1 a a a a b a a b x − − = 1 1 2 2 1 2 2 1 1 1 2 1 2 1 2 a a a a a b b a x − − = (1.2)
(後只人季 引进记号 12 1221 2122 叫做二阶行列式。它包含两行,两列
引进记号 1 1 2 2 1 2 2 1 2 1 2 2 1 1 1 2 a a a a a a a a A = = − (1.3) 叫做二阶行列式。它包含两行,两列
(後只人季 二阶行列式的计算 12 1122 12u21 22 1xX1+12x,= 对于二元线性方程组 1x1+a 21 22~2 记 2 22
11 a 12 a a12 a22 = a11a22 . − a12a21 记 , 2 1 2 2 1 1 1 2 a a a a A = + = + = . , 21 1 22 2 2 11 1 12 2 1 a x a x b a x a x b 对于二元线性方程组 二阶行列式的计算
(後只人季 二阶行列式的计算 譬如 13 1×8-3×(2)=14 28
1 8 3 ( 2) 1 4 2 8 1 3 = − − = − 譬如 二阶行列式的计算
旦 人」 学 十 十 22 2 2 十 2
+ = + = . , 2 1 1 2 2 2 2 1 1 1 1 2 2 1 a x a x b a x a x b , 2 1 2 2 1 1 1 2 a a a a A = + = + = . , 2 1 1 2 2 2 2 1 1 1 1 2 2 1 a x a x b a x a x b , 2 2 2 1 1 2 1 b a b a A =
(後只人季 x1+a12x,=b1, 11~1 21X1+2,X 21 2 11 a1x1+a12x2=b1, 211+a2x2=b2 21
+ = + = . , 21 1 22 2 2 11 1 12 2 1 a x a x b a x a x b , 2 1 2 2 1 1 1 2 a a a a A = + = + = . , 21 1 22 2 2 11 1 12 2 1 a x a x b a x a x b . 2 1 2 1 1 1 2 a b a b A =
(後只人季 则(11)的解为 12 21 22 11 21 21
则(1.1)的解为 , 2 1 2 2 1 1 1 2 2 2 2 1 1 2 1 1 a a a a b a b a A A x = = . 2 1 2 2 1 1 1 2 2 1 2 1 1 1 2 2 a a a a a b a b A A x = = (1.4)
(後只人季 三阶行列式的计算 11 13 记 21 22 32 33 1122033 aa 1223431 132132 1322u31 122133 1123032
3 1 3 2 3 3 2 1 2 2 2 3 1 1 1 2 1 3 a a a a a a a a a A = 3 1 3 2 3 3 2 1 2 2 2 3 1 1 1 2 1 3 a a a a a a a a a A = 11 22 33 = a a a . − a11a23a32 13 21 32 + a a a 12 23 31 + a a a − a13a22a31 − a12a21a33 记 三阶行列式的计算