(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let S(U)=V and T(V)=W be linear maps where U,V, W are vector spaces over the same field K. Prove :

2. Relevant equations

a) Rank (TS) <= Rank (T)

b) Rank (TS) <= Rank (S)

c) if U=V and S is nonsingular then Rank (TS) = Rank (T)

d) if V=W and T is nonsingular then Rank (TS) = Rank (S)

3. The attempt at a solution

a) TS maps to W, so is T

b) TS maps to W, but S to V, but how do I show the ranks for (a) and (b)?

c) d) So inverse of S and T exists, and err...

U,V,W are vector space over the SAME field, does that mean they have the same number of entries, say R2, R3, etc etc

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# Homework Help: Linear transformation + ranks

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