Thread: Rank in Linear Maps

Could someone please help me with this question:

Let S:U -> V, T:V->W be linear maps, where U, V, W are vector spaces over the same field K.
Prove (i) Rank(TS) <= Rank (S)
(ii) If V=W and T is non singular, then Rank(TS) = Rank(S)


Any help would be greatly appreciated!
Thank you

Originally Posted by pseudonym

Could someone please help me with this question:

Let S:U -> V, T:V->W be linear maps, where U, V, W are vector spaces over the same field K.
Prove (i) Rank(TS) <= Rank (S)

Hi there,

We have . Hence .