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Prove that if

$\mathbf{u}, \mathbf{v}$, and $\mathbf{w}$ are vectors in $R^{n}$, and if $k$ and $m$ are scalars, then: (a) $\mathbf{u}+\mathbf{v}=\mathbf{v}+\mathbf{u}$ (b) $(\mathbf{u}+\mathbf{v})+\mathbf{w}=\mathbf{u}+(\mathbf{v}+\mathbf{w})$ (c) $\mathbf{u}+\mathbf{0}=\mathbf{0}+\mathbf{u}=\mathbf{u}$ (d) $\mathbf{u}+(-\mathbf{u})=\mathbf{0}$ (e) $k(\mathbf{u}+\mathbf{v})=k \mathbf{u}+k \mathbf{v}$ (f) $(k+m) \mathbf{u}=k \mathbf{u}+m \mathbf{u}$ (g) $k(m \mathbf{u})=(k m) \mathbf{u}$ (h) $\mathbf{l u}=\mathbf{u}$
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