已知非齐次线性方程组 |} (x)_(1)+(x)_(2)+(x)_(3)+(x)_(4)=-1 4(x)_(1)+3(x)_(2)+5(x)_(3)-(x)_(4)=-1 a(x)_(1)+(x)_(2)+3(x)_(3) .,有3个线性无关的解,证明:(1)方程组系数矩阵A的秩 |} (x)_(1)+(x)_(2)+(x)_(3)+(x)_(4)=-1 4(x)_(1)+3(x)_(2)+5(x)_(3)-(x)_(4)=-1 a(x)_(1)+(x)_(2)+3(x)_(3) .;(2)当 |} (x)_(1)+(x)_(2)+(x)_(3)+(x)_(4)=-1 4(x)_(1)+3(x)_(2)+5(x)_(3)-(x)_(4)=-1 a(x)_(1)+(x)_(2)+3(x)_(3) .时, |} (x)_(1)+(x)_(2)+(x)_(3)+(x)_(4)=-1 4(x)_(1)+3(x)_(2)+5(x)_(3)-(x)_(4)=-1 a(x)_(1)+(x)_(2)+3(x)_(3) ..

已知非齐次线性方程组,有3个线性无关的解,证明:

(1)方程组系数矩阵A的秩;

(2)当时,.

参考答案与解析:

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