Question

Prove :

Let T : V -> W be a linear mapping. Then ker(T) is a subspace of V

Answer 1

let ker(T) = {v in V | Tv = 0}
1.) Is 0 in V in ker(T)?
2.) If u,v in ker(T) is u+v in ker(T)?
3.) If c is constant and v in ker(T), is cv in ker(T)?

Answer 2

1.) T(0) = 0
2.) T(u+v) = T(u) + T(v) = 0 + 0 = 0 (by linearity)
3.) T(cv) = cT(v) = c*0 = 0 (by linearity)

Answer 3

you were proving it wasnt empty? closed by addition? and scalar multiplication?

Answer 4

yah?

Answer 5

ok thank you