Section 1
C[sup(n)] as the Primary Example
Add the following two vectors:$$\left[\begin{array}{c}5+13 i \\6+2 i \\0.53-6 i \\12\end{array}\right]+\left[\begin{array}{c}7-8 i \\4 i \\2 \\9.4+3 i\end{array}\right]$$
Formally prove the associativity property.
$$\text { Scalar multiply } 8-2 i \text { with }\left[\begin{array}{c}16+23 i \\-7 i \\6 \\5-4 i\end{array}\right] \text {. }$$
$$\text { Formally prove that }\left(c_1+c_2\right) \cdot V=c_1 \cdot V+c_2 \cdot V \text {. }$$