设A为3阶方阵.且|A|=3,将A按列分块为(A1,A2,A3),计算|A3,-2A2,3A1|与|A2,3A3-2A1,A1|的值

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设A为3阶方阵.且|A|=3,将A按列分块为(A1,A2,A3),计算|A3,-2A2,3A1|与|A2,3A3-2A1,A1|的值
设A为3阶方阵.且|A|=3,将A按列分块为(A1,A2,A3),计算|A3,-2A2,3A1|与|A2,3A3-2A1,A1|的值

设A为3阶方阵.且|A|=3,将A按列分块为(A1,A2,A3),计算|A3,-2A2,3A1|与|A2,3A3-2A1,A1|的值
|A3,-2A2,3A1|
=-2×3 |A3,A2,A1|
=-6|A3,A2,A1|
=-6×(-1)|A1,A2,A3|
=6×|A|
=6×3
=18
|A2,3A3-2A1,A1|
=|A2,3A3,A1|-|A2,2A1,A1|
=3|A2,A3,A1|-0
=-3|A1,A3,A2|
=3|A1,A2,A3|
=3|A|
=3×3
=9