5 V and W be vector spaces over a field F Suppose that v 1 , , v n is a basis for V , and T L(V, W) Prove that T is injective if and only if T(v 1 ), , T(v n ) is linearly independent

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Question: 5. V and W be vector spaces over a field F. Suppose that {v 1 , . . . , v n } is a

5. V and W be vector spaces over a field F. Suppose that {v₁, . . . , v_n} is a basis for V , and T L(V, W). Prove that T is injective if and only if {T(v₁), . . . , T(v_n)} is linearly independent.

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