设向量组(alpha_{1}=(1,2,-1,0)^T,alpha_{2}=(1,1,0,2)^T,alpha_{3}=(2,1,1,a)^T,)若由(alpha_{1},alpha_{2},alpha_{3})生成的向量空间的维数为2(,)则(a)=______
举一反三
- 设向量组(alpha_{1}=(1,2,-1,0)^T,alpha_{2}=(1,1,0,2)^T,alpha_{3}=(2,1,1,a)^T,)若由(alpha_{1},alpha_{2},alpha_{3})生成的向量空间的维数为2(,)则(a)=______
- 设向量组(alpha_{1}=(1,2,-1,0)^T,alpha_{2}=(1,1,0,2)^T,alpha_{3}=(2,1,1,a)^T,)若由(alpha_{1},alpha_{2},alpha_{3})生成的向量空间的维数为2(,)则(a)=______
- 设以下三个向量组\(S_{1}\)=\(\{\alpha_{1},\alpha_{2},\alpha_{3} \},\)\(S_{2}\)=\(\{\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{4}\},\)\(S_{3}\)=\(\{\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{5}\} \)的秩依次为\(3,3,4,\)则\(S={\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{5}-\alpha_{4} }\)的秩为______ 。
- 设以下三个向量组\(S_{1}\)=\(\{\alpha_{1},\alpha_{2},\alpha_{3} \},\)\(S_{2}\)=\(\{\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{4}\},\)\(S_{3}\)=\(\{\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{5}\} \)的秩依次为\(3,3,4,\)则\(S={\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{5}-\alpha_{4} }\)的秩为______ 。
- 设以下三个向量组\(S_{1}\)=\(\{\alpha_{1},\alpha_{2},\alpha_{3} \},\)\(S_{2}\)=\(\{\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{4}\},\)\(S_{3}\)=\(\{\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{5}\} \)的秩依次为\(3,3,4,\)则\(S={\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{5}-\alpha_{4} }\)的秩为______ 。