Trong không gian véc tơ R⁵ xét tích vô hướng thông thường. Tìm một cơ sở của phần bù trực giao \[{{\rm{W}}^ \bot }\]của không gian:\[{\rm{W = span}}\left\{ {{{\rm{u}}_{\rm{1}}} = (1,2,3, - 1,2),{{\rm{u}}_{\rm{1}}} = (2,4,7,2, - 1)} \right\}\]

A. \[{{\rm{v}}_1} = (3,1,0, - 4),{{\rm{v}}_2} = (1, - 3,5,4)\]

B. \[{{\rm{v}}_1} = (4,1,0,6),{{\rm{v}}_2} = (2, - 1,3,0),{{\rm{v}}_3} = (1, - 1,3,2)\]

C. \[{{\rm{v}}_1} = (1,2,0),{{\rm{v}}_2} = (4,4,0,1)\]

D. \[{{\rm{v}}_1} = (2,4,2,0),{{\rm{v}}_2} = (5,6,1,2)\]

A. \[{{\rm{(}}{{\rm{W}}_{\rm{1}}}{\rm{ + }}{{\rm{W}}_{\rm{2}}}{\rm{)}}^ \bot }{\rm{ = }}{{\rm{W}}_{\rm{1}}}^ \bot \cap {{\rm{W}}_{\rm{2}}}^ \bot \]

B. \[{{\rm{(}}{{\rm{W}}_{\rm{1}}} \cap {\rm{ }}{{\rm{W}}_{\rm{2}}}{\rm{)}}^ \bot }{\rm{ = }}{{\rm{W}}_{\rm{1}}}^ \bot + {{\rm{W}}_{\rm{2}}}^ \bot \]

C. \[{{\rm{(}}{{\rm{W}}_{\rm{1}}} \cap {\rm{ }}{{\rm{W}}_{\rm{2}}}{\rm{)}}^ \bot }{\rm{ = }}{{\rm{W}}_{\rm{1}}}^ \bot \cup {{\rm{W}}_{\rm{2}}}^ \bot \]

D. \[{{\rm{(}}{{\rm{W}}_{\rm{1}}} \subset {\rm{ }}{{\rm{W}}_{\rm{2}}}{\rm{)}}^ \bot }{\rm{ = }}{{\rm{W}}_{\rm{1}}}^ \bot \supset {{\rm{W}}_{\rm{2}}}^ \bot \]

A. m > 1

B. \(m < \frac{1}{{\sqrt 3 }}\)

C. \[{\rm{m}} \ne 0\]

D. \[\frac{{ - 4}}{5} < {\rm{m}} < 0\]

A. m = 11

B. m = 15

C. \[{\rm{m}} \ne - 11\]

D. m = -21

A. \[{{\rm{v}}_{\rm{1}}}{\rm{ = }}{{\rm{e}}_{\rm{1}}}{\rm{ = (1, 0),}}{{\rm{v}}_{\rm{2}}}{\rm{ = }}{{\rm{e}}_{\rm{2}}}{\rm{ = (0, 1)}}\]

B. \[{{\rm{v}}_{\rm{1}}}{\rm{ = }}{{\rm{e}}_{\rm{1}}}{\rm{ = (1, 0),}}{{\rm{v}}_{\rm{2}}}{\rm{ = (2, 1)}}\]

C. \[{{\rm{v}}_{\rm{1}}}{\rm{ = (1, 2),}}{{\rm{v}}_{\rm{2}}}{\rm{ = }}{{\rm{e}}_{\rm{2}}}{\rm{ = (2, 1)}}\]

A. Hệ vô nghiệm

B. \(\left\{ {\begin{array}{*{20}{c}}{m \ne 0,}\\{m = 0}\end{array}} \right. \Rightarrow {x_1} = \frac{{ - 5{x_3} - 13{x_4} - 3}}{2};{x_1} = \frac{{ - 7{x_3} - 19{x_4} - 7}}{2}\)

C. \(\left\{ {\begin{array}{*{20}{c}}{m = 9,}\\{m \ne 9}\end{array}} \right. \Rightarrow {x_1} = \frac{{2{x_1} + 11{x_2} - 3}}{2};{x_1} = \frac{{ - 5{x_1} + 21{x_2} - 7}}{2}\)