230问答网 > 设A为m*n矩阵，且R(A)=r<n,求证：存在秩为n-r的n*(n-r)矩阵B,使AB=O

设A为m*n矩阵，且R(A)=r<n,求证：存在秩为n-r的n*(n-r)矩阵B,使AB=O

2025-02-11 04:11:47
推荐回答（2个）
回答1：

取Ax=0的基础解析。
a1,a2,...,a(n-r)
记B=（a1,a2,...,a(n-r)）
那么矩阵B是秩为n-r的n*(n-r)矩阵
且AB=0

回答2：

设未知量x为一个n*1的矩阵，即n个元素的列向量。
看方程ax=0，由于像空间a(r^n)的维数是n，而r(a)=r

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