线性代数一题设4*4矩阵A=(ab2b3b4),B=(cb2b3b4),其中a,c,b2,b3,b4均为4维列向量,且已知行列式|A|=4,|B|=1,则行列式|A+B|=?

Question

线性代数一题
设4*4矩阵A=(a b2 b3 b4),B=(c b2 b3 b4),其中a,c,b2,b3,b4均为4维
列向量,且已知行列式|A|=4,|B|=1,则行列式|A+B|=?

Answer 1

|A+B|=|a+c 2b2 2b3 2b4|
=|a 2b2 2b3 2b4|+|c 2b2 2b3 2b4|
=2^3|a b2 b3 b4|+2^3|c b2 b3 b4|
=8*4+8*1
=40
,