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。
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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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