题目

设矩阵 =((alpha )_(1),(alpha )_(2),(alpha )_(3),(beta )_(1))，=((alpha )_(1),(alpha )_(2),(alpha )_(3),(beta )_(1))，其中 =((alpha )_(1),(alpha )_(2),(alpha )_(3),(beta )_(1)) 均为 =((alpha )_(1),(alpha )_(2),(alpha )_(3),(beta )_(1)) 行 =((alpha )_(1),(alpha )_(2),(alpha )_(3),(beta )_(1)) 列的矩阵，且 =((alpha )_(1),(alpha )_(2),(alpha )_(3),(beta )_(1))，=((alpha )_(1),(alpha )_(2),(alpha )_(3),(beta )_(1))，则 =((alpha )_(1),(alpha )_(2),(alpha )_(3),(beta )_(1))=((alpha )_(1),(alpha )_(2),(alpha )_(3),(beta )_(1))（）.

题目解答

$\because$ 矩阵 $A=(\alpha_1,\alpha_2,\alpha_3,\beta_1)$ ， $B=(\alpha_1,\alpha_2,\beta_2,\alpha_3)$ ，且 $\left|A\right|=2$ ， $\left|B\right|=6$

$\therefore\left|\alpha_1,\alpha_2,\alpha_3,\beta_1\right|=2$ ， $\left | {\alpha _1,\alpha _2,\beta _2,\alpha _3} \right |=6$

故答案为： $4$