设矩阵A=(a,2r2,3r3),其中a,B,r2,r3均为3维列向量,且/A/=18,/B/=2,求/A-B/

问题描述:

设矩阵A=(a,2r2,3r3),其中a,B,r2,r3均为3维列向量,且/A/=18,/B/=2,求/A-B/

|A-B|
= |α-β,r2,2r3|
= |α,r2,2r3| + |-β,r2,2r3|
= (1/3)|α,2r2,3r3| + (-2)|β,r2,r3|
= (1/3)|A| - 2|B|
= 6 - 4
= 2