求该向量组的秩和极大线性无关组

Question

如题所述

Answer 1

A = (a1, a2, a3, a4, a5, a6) =
[ 1 2 1 1 2 0]
[-1 -2 0 3 -3 -1]
[ 1 2 2 5 2 2]
[ 5 10 5 5 13 9]
初等行变换为
[ 1 2 1 1 2 0]
[ 0 0 1 4 -1 -1]
[ 0 0 1 4 0 2]
[ 0 0 0 0 3 9]
初等行变换为
[ 1 2 0 -3 3 1]
[ 0 0 1 4 -1 -1]
[ 0 0 0 0 1 3]
[ 0 0 0 0 3 9]
初等行变换为
[ 1 2 0 -3 0 -8]
[ 0 0 1 4 0 2]
[ 0 0 0 0 1 3]
[ 0 0 0 0 0 0]
r(a1, a2, a3, a4, a5, a6) = 3,
a1, a3, a5 为 1 个极大无关组。
a2 = 2a1, a3= -3a1+4a3, a5 = -8a1+2a3+3a5本回答被提问者采纳