For the depth 2 case, Join with a levelspec can be used.

Join[coefficientMarix, {{9}, {5}, {2}}, 2]

I figured it out. If the column vector has an ArrayDepth of 1 like {9,5,2}, the following will work.

MapThread[Append, {coefficientMatrix, {9, 5, 2}}] // MatrixForm

If the column vector has an ArrayDepth of 2 like {{9},{5},{2}} then this will work:

MapThread[
  Append, {coefficientMatrix, Flatten[{{9}, {5}, {2}}]}] // MatrixForm

To get a coefficient matrix,

coefficientMatrix = {{1, 0, 5}, {-2, 2, 0}, {1, -8, -5}}
 Map[Most][
  MapThread[Append, {coefficientMatrix, {9, 5, 2}}]] // MatrixForm

and the column vector:

Map[Last][
  MapThread[Append, {coefficientMatrix, {9, 5, 2}}]] // MatrixForm

Another option is to use the Resource Functions AugmentedMatrix and CoefficientMatrix created by Dennis M Schneider.