设4阶方阵A=(a1,a2,a3,a4) ,B=(B1,a2,a3,a4),且|A|=1,|B|=2 ,则|A+B| .

题目

设4阶方阵A=(a1,a2,a3,a4) ,B=(B1,a2,a3,a4),且|A|=1,|B|=2 ,则|A+B| .

答案

|A+B| =|(a1,a2,a3,a4)+(b1,a2,a3,a4)|
=|(a1+b1),2a2,2a3,2a4)|
=2*2*2|(a1+b1),a2,a3,a4|
=8[|a1,a2,a3,a4|+|b1,a2,a3,a4|]
=8(1+2)
=24
对的.