《线性代数》课程教学资源（课件讲稿，B）第二章行列式_2-1n阶行列式的定义

三阶行列式的引出aiiar2ar3aiix+ai2x+ai3xg=bA=a21Xi+a22X2 +a23Xg =b2a22a21a23a31 +a32X +a33xg =b3a31a32a33当detA+0(A|+0)时，三元线性方程组的解为det A,det A,det A,A,AAX2X3X,[AAAdet Adet Adet A66barlaila13ar2a2a3b26b,a21a22a22a23a232a21byLba32a32a31a33a31a33加油！

  1 2 3 1 2 3 1 2 3 det 0 det det det , , det det det A A A A A A A A x x x A A A A A A         当 0 时，三元线性方程组的解为： 11 12 13 21 22 23 31 32 33 a a a A a a a a a a            1 12 13 1 2 22 23 3 32 33 b a a A b a a b a a                          31 1 32 2 33 3 3 21 1 22 2 23 3 2 11 1 12 2 13 3 1 a x a x a x b a x a x a x b a x a x a x b 11 1 13 2 21 2 23 31 3 33 a b a A a b a a b a            11 12 1 3 21 22 2 31 32 3 a a b A a a b a a b            三阶行列式的引出

推广ax +a2x +...+anx, =bAdet A,a21xi +a22X2 +...+a2nxn = b2xAdet Aanx +an2X2 +...+amx,=b2det AA.nnaia12ainXAdet Aa21azna,当 det A[4+0 时,.anianna,b,6anOb.baazna21det:,det A.b.b.amnanlaa加油！

11 12 1 21 22 2 1 1 det 0 n n n n nn a a a a a a A A a a a 当    时, 推广 1 1 1 det det det det n n n A A x A A A A x A A              1 12 1 11 12 1 2 22 21 22 2 2 1 1 1 1 1 det , , det n n n n n n nn n n n b a a a a b b a a a b a A A A A b a a a a b     11 1 12 2 1 1 21 1 22 2 2 2 1 1 2 2 n n n n n n nn n n a x a x a x b a x a x a x b a x a x a x b                   