线性代数求学霸教育:设a1,a2,a3,a,b均为4维向量,A={a1a2a3a},B={a1,a2,a3,b}.且|A|=2,|B|=3,则|A-3B|等于多少?

Question

线性代数求学霸教育:设a1,a2,a3,a,b均为4维向量,A={a1 a2 a3 a},B={a1,a2,a3,b}.且|A|=2,|B|=3,则|A-3B|
等于多少?

Answer 1

A-3B=[-2a1,-2a2,-2a3,a-3b]
|A-3B|
=|[-2a1,-2a2,-2a3,a-3b] |
=|[-2a1,-2a2,-2a3,a] |-3|[-2a1,-2a2,-2a3,b]
=(-8)|[a1,a2,a3,a] |+24|[a1,a2,a3,b] |
=-16+72
=56