Problem: If L: V -> W is linear with Ker(L) = {0} and L(V) = W. L is called an isomorphism. If {v1, v2} is a basis of V, then what can you say about {L(v1), L(v2)}?
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This means that L is both injective and surjective. Given that the kernel of L is only the zero vector, we know that L is injective. Also, since L(V) = W, we know that L is surjective. Now, let's consider the basis of V, {v_1, v_2}. Since L is a linear Show more…
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