Let X ∈ L(U, V ) and Y ∈ L(V, W). You may assume that V...

Let X ∈ L(U, V ) and Y ∈ L(V, W). You may assume that V is finite-dimensional.

1)Prove that dim(range Y) ≤ min(dim V, dim W). Explain the corresponding result for matrices in terms of rank

2) If dim(range Y) = dim V, what can you conclude of Y? Give some explanation

3) If dim(range Y) = dim W, what can you conclude of Y? Give some explanation

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Expert Solution

Colby Messinger answered 1 year ago

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