Qfwfq

[mang73]

one more please! its under you comment in the post shown here.

 

a question for Qfwfq (or anyone else who could answer)

[mang73]

Hey thanks a lot. You are a life saver. Listen, there is this Q I am trying to solve and I ahve looked into about 5 linear algebra books trying to find a similar problem so I could solve it but I can't. I am not sure if you could help me with it but here it goes:

 

Let T: V -> W be a linear map between two vector spaces. Let w0 be an element of W and let T^ -1(w0) be the set of V whose elements are mapped to w0, i.e.

 

T^ -1(w0) = { u element of V l T(u) = w0}.

 

show that

 

1) T^ -1(w0) is a subspace of V if and only if w0 is the zero element of W.

 

2) T^ -1(w0) = { v0 + v l v element of Ker(T) }, where v0 is any element in T^ -1(w0).