设向量组`\alpha _1 = (1,a,a^2),\alpha _2 = (1,b,b^2),\alpha _3 = (1,c,c^2)`,则`\alpha _1,alpha _2,alpha _3`线性无关的充分必要条件是 ( )
A. `\a,b,c`至少有两个相等
B. `\a,b,c`互不相等
C. `\a,b,c`全不为0
D. `\a,b,c`不全为0
A为3阶方阵,且\[\left| A \right| = - 2,A = \left( {\begin{array}{*{20}{c}} {{A_1}}\\ {{A_2}}\\ {{A_3}} \end{array}} \right)\],其中`\A_1`,`\A_2`,`\A_3`分别为A的1、2、3行,则\[\left| {\begin{array}{*{20}{c}} {{A_3} - 2{A_1}}\\ {3{A_2}}\\ {{A_1}} \end{array}} \right| = \]( )
A. 3
B. 4
C. 5
D. 6
已知`\alpha = (1,1,1)`,则`\|alpha ^Talpha|= `( )
A. -1
B. 0
C. 1
D. 2
已知`a,b,c,d,t\in R`,且向量组`\alpha _1 = (1,2, - 1,1),\alpha _2 = (2,0,t,0),\alpha _3 = (0, - 4,5, - 2)`能由`\beta_1=(1,a,1,b),\beta_2=(1,c,2,d)`线性表示,则`t=`( )
A. `1;`
B. `2;`
C. `3;`
D. `4.`