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Call a subset $S$ of a vector space $V$ a spanning set if $\operatorname{Span}(S)=V$. Suppose that $T: V \rightarrow W$ is a linear map of vector spaces.
a) Prove that a linear map $T$ is 1-1 if and only if $T$ sends linearly independent sets to linearly independent sets.
b) Prove that $T$ is onto if and only if $T$ sends spanning sets to spanning sets.
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