问题
单项选择题
设A是m×n矩阵,η1,η2,…,ηt是齐次方程组ATX=0的基础解系,则()。
A.t
B.n-r
C.m-t
D.n-t
答案
参考答案:C
解析:
由于A是m×n矩阵,AT就是n×m矩阵,故ATX=0是n个方程m个未知数的齐次线性方程组,故m-r(A)=t,注意r(A)=r(AT),故正确答案为C。
设A是m×n矩阵,η1,η2,…,ηt是齐次方程组ATX=0的基础解系,则()。
A.t
B.n-r
C.m-t
D.n-t
参考答案:C
解析:
由于A是m×n矩阵,AT就是n×m矩阵,故ATX=0是n个方程m个未知数的齐次线性方程组,故m-r(A)=t,注意r(A)=r(AT),故正确答案为C。
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