Question

线性代数，具体点，要过程，谢谢

Answer 1

同一类问题，做一题，其它可仿做。
3. A = (a1, a2, a3, a4, a5) =
[1 -1 0 1 2]
[1 -2 -1 3 6]
[0 -1 -1 2 4]
[0 1 1 1 1]
初等行变换为
[1 -1 0 1 2]
[0 -1 -1 2 4]
[0 -1 -1 2 4]
[0 1 1 1 1]
初等行变换为
[1 0 1 -1 -2]
[0 -1 -1 2 4]
[0 0 0 0 0]
[0 0 0 3 5]
初等行变换为
[1 0 1 0 -1/3]
[0 1 1 0 -2/3]
[0 0 0 1 5/3]
[0 0 0 0 0]
r(a1, a2, a3, a4, a5) = 3,
a1, a2, a4 是一个极大线性无关组，
a3 = a1+a2, a5 = -(1/3)a1 - (2/3)a2 + (5/3)a4
其它仿做即可。