matrix = RandomReal[{0, 9}, {5, 3}]
{{6.77034, 0.121527, 5.26578}, {5.34336, 6.89392, 5.95391}, {2.3593,
1.71727, 4.31392}, {4.91466, 7.65461, 7.16075}, {6.91384, 5.82546,
6.50945}}
MapAt[Floor, matrix, {All, 1 ;; 2}]
(* or *)
MapAt[Floor, #, {{1}, {2}}] & /@ matrix
(* or *)
{Floor@#1, Floor@#2, ##3} & @@@ matrix
(* or *)
{Floor@#1, Floor@#2, #3} & @@@ matrix
(* or *)
{Floor@#[[1]], Floor@#[[2]], #[[3]]} & /@ matrix
(* or *)
Replace[matrix, {a_, b_, c__} -> {Floor@a, Floor@b, c}, {1}]
All give
{{6, 0, 5.26578}, {5, 6, 5.95391}, {2, 1, 4.31392}, {4, 7,
7.16075}, {6, 5, 6.50945}}