質問: matrix question prove that the following determinant equals zero without expanding the determinant —a-b b-c c-a— —b-c c-a a-b— —c-a a-b b-c—
回答: prove that the following determinant equalszero without expanding the determinant |a-b b-c c-a| |b-c c-a a-b| |c-a a-b b-c| sol|a-b b-c c-a|*1────── |b-c c-a a-b|<───────| |c-a a-b b-c| | a-b b-c c-a| =|a-b+b-c b-c+c-a c-a+a-b| | c-a a-b b-c| |a-b b-c c-a| =|a-c b-a c-b|*1────── |c-a a-b b-c|<───────| | a-b b-c c-a| =| a-c b-a c-b| |a-c+c-a b-a+a-b c-b+b-c| |a-b b-c c-a| =|a-c b-a c-b| | 0 0 0| =0