Is T(inv)(0) a Subspace of V and T(V) a Subspace of W?

[mang733]

Could someone help me here please?

Let V and W be two vector spaces and T: V -> W be a linear map. Define

T(inv) (0) = { u element of V l T(u) = 0 }

where 0 is the zero element in W. Also define,

T(V) = { T(u) l u element of V},

the image of V under T. Show that T(inv) (0) is a subspace of V and T(V) is a subspace of W.

Your help is much appreciated!

 

[matt grime]

Just chekc the axioms for a subspave are satisfied, and post your working.

 

[mang733]

you mean the three axioms?

 

[mang733]

since I want to make sure I have the correct answer, if someone has the time I appreciate a detailed response.

 

[matt grime]

Doing someone else's homework isn't very interesting to most people. So post what you've managed to verify. Something is a subspace if and only iof it satisfies the rules for being a subspace; how far have you been able to verify that the rules hold?