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

Prove that if T, S : V -> W are linear and W is finite dimensional then

dim (range(S + T)) <= dim range S + dim range T

2. Relevant equations

3. The attempt at a solution

I know that the dim range S + dim range T can be at most 2 * dim W. However, I'm a little stuck on trying to figure out what dim (range(S+T)) is. How do I determine S + T?

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# Homework Help: Proof regarding Range of linear maps

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