Final answer:
To find the column vector from point a at (1,1) to point b at (8,7), subtract the coordinates of a from b to obtain the column vector \(\begin{pmatrix}7\\6\end{pmatrix}\).
Step-by-step explanation:
To write point a at (1,1) and point b at (8,7) as a column vector a to b, we first find the difference between the x-coordinates and y-coordinates of the two points, respectively. Subtract the x-coordinate of point a from the x-coordinate of point b to get the x-component of the vector, and subtract the y-coordinate of point a from the y-coordinate of point b for the y-component. The resulting column vector is:
\[\begin{pmatrix}8 - 1\\7 - 1\end{pmatrix} = \begin{pmatrix}7\\6\end{pmatrix}\]
So, the column vector from point a to point b is \(\begin{pmatrix}7\\6\end{pmatrix}\).