Galactica test Ka’Chava

Suppose \(T\) is a function from \(V\) to \(W\). Let the “graph” of \(T\) be the subset of \(V \times W\) such that:

\begin{equation} graph\ T = \{(v,Tv) \in V \times W \mid v \in V\} \end{equation}

Show that \(T\) is a linear map IFF the graph of \(T\) is a subspace of \(V \times W\).

Review: A Linear Map

Recall that a function \(T: V \to W\) is called a linear map if it is a map that…

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