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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.

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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.
in Mathematics by Platinum (101k points) | 305 views

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