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    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)


    Thank you!
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    What have you done so far? What are your thoughts?
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    sorry firstly I just realised that I posted a smiley where it's suppose to be a U.

    I'm thinking Rank(TS) is T: U -> W so it's less than or equal to dim(U) by the dimension theorem, and maybe incorporate somehow the fact that Rank(S) is also less than or equal to dim(U)...
    As for part 2, I honestly dont even know where to begin...
 
 
 
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Updated: February 8, 2010
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