已知矩阵n=107014110122001,A=(aij)n*n,aij=i^2+j^2,求A的行列式和秩?

Question

已知矩阵n=107014110122001,A=(aij)n*n,aij=i^2+j^2 ,求A的行列式和秩?

Answer 1

由已知,A =1^2+1^2 1^2+2^2 1^2+3^2 ...1^2+n^22^2+1^2 2^2+2^2 2^2+3^2 ...2^2+n^23^2+1^2 3^2+2^2 3^2+3^2 ...3^2+n^2..n^2+1^2 n^2+2^2 n^2+3^2 ...n^2+n^2ri-r(i-1),i=n,n-1,...,2 (即从最后一行开始,每行减上一...