三阶矩阵[1,1,1；x1,x2,x3;x1^2,x2^2,x3^2]=(x2-x1)(x3-x1)(x3-x2)是怎么化简得到的?

Question

三阶矩阵 [1,1,1；x1,x2,x3; x1^2,x2^2,x3^2]=(x2-x1)(x3-x1)(x3-x2)是怎么化简得到的?

Answer 1

r3-x1r2, r2-x1r1
1 1 1
0 x2-x1 x3-x1
0 x2(x2-x1) x3(x3-x1)
r3-x2r2
1 1 1
0 x2-x1 x3-x1
0 0 (x3-x1)(x3-x2)
行列式 = (x2-x1)(x3-x1)(x3-x2).
事实上, 这是3阶的Vandermonde行列式.
学过行列式按行列展开定理后, 会有n阶的结果 .
满意请采纳^_^