Theorem

Suppose T is a linear map from V to W. Then T(0) = 0.

Proof

By additivity, we have \({latex.inline[T(0) = T(0 + 0) = T(0) + T(0)](T(0) = T(0 + 0) = T(0) + T(0))}. We can subtract the inverse of T(0) from both sides to get that \){latex.inlineT(0) = 0}.