Coset-Example

[mathmari]

Hi!!!

I have the following exercise: describe the set of solutions of a linear system as a coset of an appropriate subspace.

Could you give me an example?

[studiot]

Well a coset is a subspace plus an additional element(s)

 

The kernel is a subspace but not necessarily the whole solution

 

So whole solution is the kernel plus .....

 

Does this help?

[mathmari]

Is the whole solution the kernel plus a particular solution?

So if [tex] Ax_{0}=0 [/tex] and w is a soluion of [tex] Ax=b [/tex], then the whole solution is [tex] x_{0}+w [/tex] ??