Homogeneous system

Homogenous system "Ax = 0"

 

1) trivial solution :  x = 0

-> Span {0}

2) nontrivial solution : equation has at least one free variable (=해가 무한대)

-> Ax = 0 은 항상 Span {v1, ..., vp} 로 표현될 수 있다.

 

 

Nonhomogenouse system "Ax = b"

 

- 정리 6

Ax = b is consistent and let p be a solution

Then the solution set of Ax = b is the set of all vectors of the form w = p + vh

where vh is any solution of the homogeneous equation Ax = 0

 

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