A is a matrix of order n, α 1, α 2 α n is n-dimensional sequence vector, α n ≠ 0, a α 1 = α 2 ,Aαn-1=αn,Aα

A is a matrix of order n, α 1, α 2 α n is n-dimensional sequence vector, α n ≠ 0, a α 1 = α 2 ,Aαn-1=αn,Aα

Let a ^ (n-k) α k = α n ≠ 0 and a ^ (n-k + 1) α k = a α n = 0 prove that α 1, α 2,..., α n are linearly independent. Let K1 α 1 + K2 α 2 +... + kn α n = 0 multiply a ^ (n-1) left by both sides of the upper formula, and get K1 α n = 0. Since α n ≠ 0, K1 = 0, so K2 α 2 +... + kn α n = 0. Similarly, let a ^ (n-2) multiply a ^ (n-2) left by