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**Drexel28** I'll give __hints__

The first part is trivial if you know the rank-nullity theorem since, if $\displaystyle V$ is an $\displaystyle F$-space then a linear functional $\displaystyle \varphi:V\to F$ can be viewed as a linear transformation with $\displaystyle F$ viewed as a one dimensional vector space over itself.

Otherwise, try to show that if $\displaystyle \varphi(x_0)\ne 0$ then $\displaystyle V=\text{span}\{x_0\}\oplus\ker\varphi$.

For the other part, what if $\displaystyle W$ is an $\displaystyle n-1$ dimensional subspace of $\displaystyle V$ and you considered some complement to it $\displaystyle \text{span}\{x_0\}$. Then, what if you considered the mapping $\displaystyle \varphi:V\to W:w+\alpha x_0\mapsto \alpha$?