Let $\mathbf{u}, \mathbf{v}$, and $\mathbf{w}$ be vectors in $\mathbb{R}^{n}$ and let $c$ and $d$ be 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. $\mathbf{u}+\mathbf{0}=\mathbf{u}$ d. $\mathbf{u}+(-\mathbf{u})=\mathbf{0}$ e. $c(\mathbf{u}+\mathbf{v})=c \mathbf{u}+c \mathbf{v}$ f. $(c+d) \mathbf{u}=c \mathbf{u}+d \mathbf{u}$ g. $c(d \mathbf{u})=(c d) \mathbf{u}$ h. $1 \mathbf{u}=\mathbf{u}$ Commutativity Associativity Distributivity Distributivity Simplify the given vector expression. Indicate which properties in the theorem above \[ \begin{array}{rlrl} 2(\mathbf{a}-5 \mathbf{b})+5(2 \mathbf{b}+\mathbf{a}) & \\ 2(\mathbf{a}-5 \mathbf{b})+5(2 \mathbf{b}+\mathbf{a}) & =(2 \mathbf{a}-10 \mathbf{b})+(10 \mathbf{b}+5 \mathbf{a}) & \text { properties ? } \\ & =(2 \mathbf{a}+5 \mathbf{a})+(10 \mathbf{b}-10 \mathbf{b}) \text { properties ? } \end{array} \]