1. Determine if the following statements are true or false. If a
statement 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 φ: V → W be a linear transformation.
A) If φ is injective, then dim(V) ≤ dim(W).
B) If dim(V) ≤ dim(W), then φ is injective.
C) If φ is surjective, then dim(V) ≥ dim(W).
D) If dim(V) ≥...