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1. Determine if the following statements are true or false. If a statement is true, prove...

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Advance Math

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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