Answer
See below
Work Step by Step
Let $v, w \in V$ and $k \in R$ scalar.
$$T(v+w)=(u,v+w)\\
=(u,v)+(u,w)\\
=T(v)+T(w)$$
$$T(kv)=(u,kv)\\
=k(u,v) \\
=kT(v)$$
It is a linear transformation.
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