Question

线性代数 第三题求解 要过程

Answer 1

A = (a1, a2, a3, a4, a5) =
[1 7 2 5 2]
[3 0 -1 1 -1]
[2 14 0 6 4]
[0 3 1 2 1]
初等行变换为
[1 7 2 5 2]
[0 -21 -7 -14 -7]
[0 0 -4 -4 0]
[0 3 1 2 1]
初等行变换为
[1 7 2 5 2]
[0 3 1 2 1]
[0 0 1 1 0]
[0 0 0 0 0]
初等行变换为
[1 7 0 3 2]
[0 3 0 1 1]
[0 0 1 1 0]
[0 0 0 0 0]
初等行变换为
[1 0 0 2/3 -1/3]
[0 1 0 1/3 1/3]
[0 0 1 1 0]
[0 0 0 0 0]
a1, a2, a3 是一个极大线性无关组
a4 = (2/3)a1+(1/3)a2+a3
a5 = (a2-a1)/3