求行列式,设a1 b1 c1;a2 b2 c2;a3 b3 c3=3 ,则 a1+3b1 c1 b1;a2+3b2 c2 b2;a3+3b3 c3 b3 =

题目

求行列式,设a1 b1 c1;a2 b2 c2;a3 b3 c3=3 ,则 a1+3b1 c1 b1;a2+3b2 c2 b2;a3+3b3 c3 b3 =

答案

a1+3b1 c1 b1
a2+3b2 c2 b2
a3+3b3 c3 b3
= 第1列减3倍的第3列
a1 c1 b1
a2 c2 b2
a3 c3 b3
第2,3列交换
= -1*
a1 b1 c1
a2 b2 c2
a3 b3 c3
= -3.