Question

Let f:V->W be a linear transformation. Show that the nullspace of f is a subspace of V and that the image of f is a subspace of W.

Answer 1

are you stuck on both parts?

Answer 2

yea. don't know where or how to start showing it. :/

Answer 3

ok...

Answer 4

for the first one let \[N=\{v\in V|f(v)=0\}\]

Answer 5

we need to show 1) N is nonempty

Answer 6

2) is \[v,w\in V\] then \[v+w\in V\]

Answer 7

not is...if

Answer 8

lets try 2) again
if \[u,v\in N\] then \[v+u\in N\]

Answer 9

3) if \[v\in N\] and c is any scalar then \[cv\in N\]

Answer 10

can you show any of those 3?

Answer 11

oh okay. yup i can. (: