计算行列式|a-b-c 2a 2a| |2b b-a-c 2b| |2c.2c.C-a-b|

问题描述:

计算行列式|a-b-c 2a 2a| |2b b-a-c 2b| |2c.2c.C-a-b|

|a-b-c 2a 2a| |2b b-a-c 2b| |2c.2c.C-a-b|
=|a+b+c a+b+c a+b+c| |2b b-a-c 2b| |2c.2c.C-a-b|
=(a+b+c)|1 1 1| |0 -b-a-c 0| |0.0.-C-a-b|
=(a+b+c)^3