Question

求解一道线性代数的问题

求解一道线性代数的问题第三题求解要步骤谢谢大神

Answer 1

3. A = (a1, a2, a3, a4, a5) =
[ 1 2 1 1 3]
[-1 1 2 -1 0]
[ 0 5 5 -2 7]
[ 4 6 2 0 14]
初等行变换为
[ 1 2 1 1 3]
[ 0 3 3 0 3]
[ 0 5 5 -2 7]
[ 0 -2 -2 -4 2]
初等行变换为
[ 1 0 -1 1 1]
[ 0 1 1 0 1]
[ 0 0 0 -2 2]
[ 0 0 0 -4 4]
初等行变换为
[ 1 0 -1 0 2]
[ 0 1 1 0 1]
[ 0 0 0 1 -1]
[ 0 0 0 0 0]
r(A) = 3, a1, a2, a4 为一个极大无关组，
a3 = a2 - a1
a5 = 2a1+a2-a4