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**Prove that G is a subspace of V ⊕ V and the quotient space (V ⊕ V) / G is isomorphic to V.**

Let $V$ be a vector space over $\Bbb{F}$, and let $T : V \rightarrow V$ be a linear operator on $V$. Let $G$ be the subset of $V \oplus V$ consisting of all ordered pairs $(x, T(x))$ for $x$ in $V$. I don't really understand what I am supposed to do. Is $G$ a subset of $V \oplus V$ or a subset of the ordered pairs $(x, T(x))$. Please help.