the format for the columnized vector is just about the same representation for a matrix, and so its operations will be about just the same
[tex]a = \begin{bmatrix} 4\\1 \end{bmatrix}\qquad b= \begin{bmatrix} 3\\2 \end{bmatrix} \\\\[-0.35em] ~\dotfill\\\\ a+b\implies \begin{bmatrix} 4\\1 \end{bmatrix}+\begin{bmatrix} 3\\2 \end{bmatrix}\implies \begin{bmatrix} 4+3\\ 1+2 \end{bmatrix}\implies \begin{bmatrix} 7\\3 \end{bmatrix} \\\\[-0.35em] ~\dotfill[/tex]
[tex]2a-b\implies 2\begin{bmatrix} 4\\1 \end{bmatrix}-\begin{bmatrix} 3\\2 \end{bmatrix}\implies \begin{bmatrix} 2\cdot 4\\2\cdot 1 \end{bmatrix}-\begin{bmatrix} 3\\2 \end{bmatrix} \\\\\\ \begin{bmatrix} 8\\2 \end{bmatrix}-\begin{bmatrix} 3\\2 \end{bmatrix}\implies \begin{bmatrix} 8-3\\2-2 \end{bmatrix}\implies \begin{bmatrix} 5\\0 \end{bmatrix}[/tex]
