Tìm x, y, z sao cho có thể biểu diễn thành tổ hợp tuyến tính sau \[\left( {2, - 5,3} \right) = x\left( {1, - 3,2} \right) + y\left( {2, - 4, - 1} \right) + z\left( {1, - 5,7} \right)\]

A. Điều nào sau đây không đúng?

A. Hệ các véc tơ cột của A là một hệ trực chuẩn

B. Hệ các véc tơ hàng của A là một hệ trực chuẩn

C. Định thức của A luôn bằng 1

D. Tồn tại ma trận nghịch đảo A-1=At

A. \[{v_1} = \left( {3,1,0, - 4} \right),{v_2} = \left( {1, - 3,5,4} \right)\]

B. \[{v_1} = \left( {4,1,0,6} \right),{v_2} = \left( {2, - 1,3,0} \right),{v_3} = \left( {1, - 1,3,2} \right)\]

C. \[{v_1} = \left( {1,2,0} \right),{v_2} = \left( {4,4,0,1} \right)\]

D. \[{v_1} = \left( {2,4,2,0} \right),{v_2} = \left( {5,6,1,2} \right)\]

A. \[{v_1} = \left( {\frac{1}{3},\frac{2}{3},\frac{2}{3}} \right),{v_2} = \left( {0,\frac{1}{{\sqrt 2 }},\frac{{ - 1}}{{\sqrt 2 }}} \right),{v_3} = \left( {\frac{{ - 4}}{{\sqrt {18} }},\frac{1}{{\sqrt {18} }},\frac{1}{{\sqrt {18} }}} \right),\alpha = 9,\beta = 18,\gamma = 18\]

B. \[{v_1} = \left( {\frac{1}{{\sqrt 3 }},\frac{{ - 1}}{{\sqrt 3 }},\frac{1}{{\sqrt 3 }}} \right),{v_2} = \left( {\frac{1}{{\sqrt 2 }},\frac{1}{{\sqrt 2 }},0} \right),{v_3} = \left( {\frac{1}{{\sqrt 6 }},\frac{1}{{\sqrt 6 }},\frac{{ - 2}}{{\sqrt 6 }}} \right),\alpha = 5,\beta = 10,\gamma = 10\]

C. \[{v_1} = \left( {\frac{2}{3},\frac{2}{3},\frac{{ - 1}}{3}} \right),{v_2} = \left( {\frac{1}{3},\frac{{ - 2}}{3},\frac{{ - 2}}{3}} \right),{v_3} = \left( {\frac{2}{3},\frac{1}{3},\frac{2}{3}} \right),\alpha = 3,\beta = 5,\gamma = - 1,p = 1,q = 2\left( {\begin{array}{*{20}{c}}\begin{array}{l}2\\0\end{array}&\begin{array}{l} - 6\\1\end{array}\end{array}} \right)\]

D. \[{v_1} = \left( {\frac{2}{3},\frac{2}{3},\frac{{ - 1}}{3}} \right),{v_2} = \left( {\frac{1}{3},\frac{{ - 2}}{3},\frac{2}{3}} \right),{v_3} = \left( {\frac{2}{3},\frac{1}{3},\frac{2}{3}} \right),\alpha = 1,\beta = 1,\gamma = 2\]

B.  \[\left\{ \begin{array}{l}m \ne 0\\m = 0\end{array} \right. \Rightarrow {x_1} = \frac{{ - 5{x_2} - 13{x_4} - 3}}{2};{x_1} = \frac{{ - 7{x_3} - 19{x_4} - 7}}{2}\]

A. \[det\left( {kA} \right) = kdet\left( A \right)\]

B. \[det\left( {A + B} \right) = det\left( A \right) + det\left( B \right)\]

C. \[det\left( {AB} \right) = det\left( A \right)det\left( B \right)\]

D. \[det\left( { - A} \right) = - det\left( A \right)\]

A. \[\left\{ {{v_1} = \left( {2, - 1,0,0,0} \right),{v_2} = \left( { - 17,0,5,0,1} \right),{v_3} = \left( {13,0, - 4,1,0} \right)} \right\}\]

B. \[\left\{ {{v_1} = \left( {2, - 1,0,0,0} \right),{v_2} = \left( { - 17,0,5,0,1} \right)} \right\}\]

C. \[\left\{ {{v_1} = \left( {2, - 1,0,0,0} \right),{v_2} = \left( {7,0,5,0,1} \right),{v_3} = \left( {13,0, - 4,1,0} \right)} \right\}\]

D. \[\left\{ {{v_1} = \left( {2, - 1,0,0,0} \right),{v_2} = \left( { - 17,0,5,0,1} \right),{v_3} = \left( {15,1, - 5,0, - 1} \right)} \right\}\]

A.\[{v_1} = \left( {\frac{1}{{\sqrt 3 }},\frac{{ - 1}}{{\sqrt 3 }},\frac{1}{{\sqrt 3 }}} \right),{v_2} = \left( {\frac{1}{{\sqrt 2 }},\frac{1}{{\sqrt 2 }},0} \right),{v_3} = \left( {\frac{1}{{\sqrt 6 }},\frac{1}{{\sqrt 6 }},\frac{{ - 2}}{{\sqrt 6 }}} \right),\alpha = - 5,\beta = 1,\gamma = 1,p = 1,q = 2\]

B. \[{v_1} = \left( {\frac{1}{{\sqrt 3 }},\frac{1}{{\sqrt 3 }},\frac{1}{{\sqrt 3 }}} \right),{v_2} = \left( {\frac{1}{{\sqrt 2 }},\frac{{ - 1}}{{\sqrt 2 }},0} \right),{v_3} = \left( {\frac{1}{{\sqrt 6 }},\frac{1}{{\sqrt 6 }},\frac{{ - 2}}{{\sqrt 6 }}} \right),\alpha = - 5,\beta = - 1,\gamma = - 1\]

C. \[{v_1} = \left( {\frac{2}{3},\frac{2}{3},\frac{{ - 1}}{3}} \right),{v_2} = \left( {\frac{1}{3},\frac{{ - 2}}{3},\frac{{ - 2}}{3}} \right),{v_3} = \left( {\frac{2}{3},\frac{1}{3},\frac{2}{3}} \right),\alpha = - 3,\beta = - 1,\gamma = - 1\]

D. \[{v_1} = \left( {\frac{2}{3},\frac{2}{3},\frac{{ - 1}}{3}} \right),{v_2} = \left( {\frac{1}{3},\frac{{ - 2}}{3},\frac{{ - 2}}{3}} \right),{v_3} = \left( {\frac{2}{3},\frac{1}{3},\frac{2}{3}} \right),\alpha = 5,\beta = 5,\gamma = - 1\]