- #1
Mr Davis 97
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Homework Statement
T/F: Let ##T: V \rightarrow W##. If ##\{v_1,v_2,...,v_k \}## is a linearly independent set, then ##\{T(v_1), T(v_2),..., T(v_k) \}## is linearly independent.
Homework Equations
The Attempt at a Solution
This seems to be true, because we know that ##a_1v_1 + a_2v_2 + \cdots + a_k v_k = 0## has only the trivial solution, since they are linearly independent. Then if we apply ##T## to both sides, we get that ##a_1T(v_1) + a_2T(v_2) + \cdots + a_kT(v_k) = 0##, which should mean that this only has the trivial solution as well, right? Meaning that they are linearly independent?