引入W112a11a22a33 +a12a23a31 +a13a21a32-b20/21—a11a2332—a1221a33—a1322a311312= ai(a22a33 -a23a32) + a12(a23a31 -a21a33+ a13 (a2132 - a2231)a,aa23a23a21 a23-a12[a31 a33]+ a13a31 a33=a[a32a33]可见，三级行列式可通过二级行列式来表示。RS2.6行列式按一行（列）展开§2.6 行列式按一行（列）展开 引入 1 1 2 3 3 2 1 2 2 1 3 3 1 3 2 2 3 1, 1 1 2 2 3 3 1 2 2 3 3 1 1 3 2 1 3 2 a a a a a a a a a a a a a a a a a a − − − = + + 31 32 33 21 22 23 11 12 13 a a a a a a a a a ( ) = a11 a22a33 − a23a32 ( ) + a12 a23a31 − a21a33 ( ) + a13 a21a32 − a22a31 22 23 11 32 33 a a a a a = 可见，三级行列式可通过二级行列式来表示． 21 23 12 31 33 a a a a a − 21 23 13 31 33 a a a a a +