Tìm véc tơ u sau của không gian R⁴ thỏa mãn phương trình: \[{\rm{3(}}{{\rm{v}}_{\rm{1}}} - {\rm{u) + 2(}}{{\rm{v}}_{\rm{2}}}{\rm{ + u) = 5(}}{{\rm{v}}_{\rm{3}}}{\rm{ + u)}}\]trong đó \[{\rm{v}}1 = \left( {2,5,1,3} \right);{\rm{v}}2 = \left( {10,1,5,10} \right);{\rm{v}}3 = (4,1, - 1,1)\]

A. \[{\rm{\lambda }} = 10\]

B. \[{\rm{\lambda }} = - 11\]

C. \[{\rm{\lambda }} = 12\]

D. \[{\rm{\lambda }} = 11\]

A. \[{\rm{\lambda }} = 1\]

B. \[{\rm{\lambda }} = 1,{\rm{\lambda }} = \frac{1}{2}\]

C. \[{\rm{\lambda }} = 2,{\rm{\lambda }} = \frac{1}{2}\]

D. \[{\rm{\lambda }} = - 3\]

A. Các véc tơ (x, y, z) thoả mãn\[{\rm{x}} \le {\rm{y}} \le {\rm{z}}\]

B. Các véc tơ (x, y, z) thoả mãn x + y + z = 0

C. Các véc tơ (x, y, z) thoả mãn xy = 0

D. Các véc tơ (x, y, z) thoả mãn 3x + 2y - 4z = 0

A. \[{{\rm{x}}_1} = 2,{{\rm{x}}_2} = 1,{{\rm{x}}_3} = 2,{{\rm{x}}_4} = 1\]

B. \[{{\rm{x}}_1} = - 3,{{\rm{x}}_2} = 1,{{\rm{x}}_3} = 2,{{\rm{x}}_4} = - 1\]

C. \[{{\rm{x}}_1} = - 3,{{\rm{x}}_2} = - 1,{{\rm{x}}_3} = 2,{{\rm{x}}_4} = - 1\]

D. \[{{\rm{x}}_1} = 4,{{\rm{x}}_2} = - 5,{{\rm{x}}_3} = 7,{{\rm{x}}_4} = 3\]

A. \(\left\{ {\begin{array}{*{20}{c}}{(x,y,z) + (x\prime ,y\prime ,x\prime ) = (x + x\prime ,y + y\prime ,z + z\prime }\\{\alpha (x,y,z) = (\alpha x,y,z);\alpha \in R}\end{array}} \right.\)

B. \(\left\{ {\begin{array}{*{20}{c}}{(x,y,z) + (x\prime ,y\prime ,x\prime ) = (x + x\prime ,y + y\prime ,z + z\prime )}\\{\alpha (x,y,z) = (2\alpha x,2\alpha y,2\alpha z);\alpha \in R}\end{array}} \right.\)

C. \(\left\{ {\begin{array}{*{20}{c}}{(x,y,z) + (x\prime ,y\prime ,x\prime ) = (x + x\prime + 1,y + y\prime + 1,z + z\prime + 1)}\\{\alpha (x,y,z) = (0,0,0);\alpha \in R}\end{array}} \right.\)

D. \(\left\{ {\begin{array}{*{20}{c}}{(x,y,z) + (x\prime ,y\prime ,x\prime ) = (x + x\prime ,y + y\prime ,z + z\prime )}\\{\alpha (x,y,z) = (\alpha x,\alpha y,\alpha z);\alpha \in R}\end{array}} \right.\)

A. \[{\rm{u}} = (1, - 2,1),{\rm{v}} = (2,1, - 1)\]

B. \[{\rm{u}} = (2, - 3,13),{\rm{v}} = (2,0,8),{\rm{w}} = (8, - 1,8),{\rm{x}} = (3, - 9,7)\]

C. \[{\rm{u}} = (1,1,1),{\rm{v}} = (1,2,3),{\rm{w}} = (2, - 1,1)\]

D. \[{\rm{u}} = (1,1,2),{\rm{v}} = (1,2,5),{\rm{w}} = (5,3,4)\]