Suppose V, W are finite dimensional, T e L(V, W), and dim range T >= 1. Prove that if{W1,.....Wm} is any basis for W, there is a corresponding basis, {v1, ..., Vn} for V such that the matrix of T with respect to these bases satisfies M(T)1,. = ei E F^n where e, is the first standard basis vector.

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