1. Determine if the following statements are true or false. If astatement is true, prove it in general, If a statement is false,provide a specific counterexample.
Let V and W be finite-dimensional vector spaces over field F,and let ?: V ? W be a linear transformation.
A) If ? is injective, then dim(V) ? dim(W).
B) If dim(V) ? dim(W), then ? is injective.
C) If ? is surjective, then dim(V) ? dim(W).
D) If dim(V) ? dim(W), then ? is surjective.
E) If V = {0} , then ? is injective.
F) If dim(V) NOT= dim(W), then ? is not bijective.
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