Question: How to prove this question on linear transformation? Let T:R^m -> R^n be a linear transformation, and let u and v be two vectors in

How to prove this question on linear transformation?

Let T:R^m -> R^n be a linear transformation, and let u and v be two vectors in R^m. Prove that if the set {T(u),T(v)} is linearly independent that the set {u,v} is linearly independent. (Hint: What equation do you need to solve to show {u,v} is linearly independent? What happens to this equation if you apply T to both sides?)

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