5 deleted 2 characters in body
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For the version of the question before Edit 2:

m = Range[0, 5];
a = -Range[15];
Pick[m, NonPositive[Max[# + a - 1] & /@ m]]
(* or Select[m, NonPositive[Max[# + a - 1]]&] *)

{0, 1, 2}

Update: For the general case, with M and A as in OP's Edit 2, simply change # + a -1 to #.Transpose[A] - 1:

Pick[M, NonPositive[Max[#.Transpose[A] - 1]& /@ M]]
(* or Pick[M, UnitStep[1 - Max[#.Transpose[A]]] & /@ M, 1] *)
(* or Select[M, NonPositive[Max[#.Transpose[A] - 1]]&] *)

all give

{{0,0,0,1}, {-(1/2),-(1/2),-(1/2),1/2}, {-(1/2),1/2,1/2,1/2}, {1/2,-(1/2),1/2,1/2}, <<9>>, {-(1/2),1/2,-(1/2),-(1/2)}, {1/2,-(1/2),-(1/2),-(1/2)}, {0,0,0,-1}}

For the version of the question before Edit 2:

m = Range[0, 5];
a = -Range[15];
Pick[m, NonPositive[Max[# + a - 1] & /@ m]]
(* or Select[m, NonPositive[Max[# + a - 1]]&] *)

{0, 1, 2}

Update: For the general case, with M and A as in OP's Edit 2, simply change # + a -1 to #.Transpose[A] - 1:

Pick[M, NonPositive[Max[#.Transpose[A] - 1]& /@ M]]
(* or Pick[M, UnitStep[1 - Max[#.Transpose[A]]] & /@ M, 1] *)
(* or Select[M, NonPositive[Max[#.Transpose[A] - 1]]&] *)

{{0,0,0,1}, {-(1/2),-(1/2),-(1/2),1/2}, {-(1/2),1/2,1/2,1/2}, {1/2,-(1/2),1/2,1/2}, <<9>>, {-(1/2),1/2,-(1/2),-(1/2)}, {1/2,-(1/2),-(1/2),-(1/2)}, {0,0,0,-1}}

For the version of the question before Edit 2:

m = Range[0, 5];
a = -Range[15];
Pick[m, NonPositive[Max[# + a - 1] & /@ m]]
(* or Select[m, NonPositive[Max[# + a - 1]]&] *)

{0, 1, 2}

Update: For the general case, with M and A as in OP's Edit 2, simply change # + a -1 to #.Transpose[A] - 1:

Pick[M, NonPositive[Max[#.Transpose[A] - 1]& /@ M]]
Pick[M, UnitStep[1 - Max[#.Transpose[A]]] & /@ M, 1] 
Select[M, NonPositive[Max[#.Transpose[A] - 1]]&] 

all give

{{0,0,0,1}, {-(1/2),-(1/2),-(1/2),1/2}, {-(1/2),1/2,1/2,1/2}, {1/2,-(1/2),1/2,1/2}, <<9>>, {-(1/2),1/2,-(1/2),-(1/2)}, {1/2,-(1/2),-(1/2),-(1/2)}, {0,0,0,-1}}

4 added 69 characters in body
source | link

For the version of the question before Edit 2:

m = Range[0, 5];
a = -Range[15];
Pick[m, NonPositive[Max[# + a - 1] & /@ m]]
(* or Select[m, NonPositive[Max[# + a - 1]]&] *)

{0, 1, 2}

Update: For the general case, with M and A as in OP's Edit 2, simply change # + a -1 to #.Transpose[A] - 1:

Pick[M, NonPositive[Max[#.Transpose[A] - 1]& /@ M]]
(* or Pick[M, UnitStep[1 - Max[#.Transpose[A]]] & /@ M, 1] *)
(* or Select[M, NonPositive[Max[#.Transpose[A] - 1]]&] *)

{{0,0,0,1}, {-(1/2),-(1/2),-(1/2),1/2}, {-(1/2),1/2,1/2,1/2}, {1/2,-(1/2),1/2,1/2}, <<9>>, {-(1/2),1/2,-(1/2),-(1/2)}, {1/2,-(1/2),-(1/2),-(1/2)}, {0,0,0,-1}}

For the version of the question before Edit 2:

m = Range[0, 5];
a = -Range[15];
Pick[m, NonPositive[Max[# + a - 1] & /@ m]]
(* or Select[m, NonPositive[Max[# + a - 1]]&] *)

{0, 1, 2}

Update: For the general case, with M and A as in OP's Edit 2, simply change # + a -1 to #.Transpose[A] - 1:

Pick[M, NonPositive[Max[#.Transpose[A] - 1]& /@ M]]
(* or Select[M, NonPositive[Max[#.Transpose[A] - 1]]&] *)

{{0,0,0,1}, {-(1/2),-(1/2),-(1/2),1/2}, {-(1/2),1/2,1/2,1/2}, {1/2,-(1/2),1/2,1/2}, <<9>>, {-(1/2),1/2,-(1/2),-(1/2)}, {1/2,-(1/2),-(1/2),-(1/2)}, {0,0,0,-1}}

For the version of the question before Edit 2:

m = Range[0, 5];
a = -Range[15];
Pick[m, NonPositive[Max[# + a - 1] & /@ m]]
(* or Select[m, NonPositive[Max[# + a - 1]]&] *)

{0, 1, 2}

Update: For the general case, with M and A as in OP's Edit 2, simply change # + a -1 to #.Transpose[A] - 1:

Pick[M, NonPositive[Max[#.Transpose[A] - 1]& /@ M]]
(* or Pick[M, UnitStep[1 - Max[#.Transpose[A]]] & /@ M, 1] *)
(* or Select[M, NonPositive[Max[#.Transpose[A] - 1]]&] *)

{{0,0,0,1}, {-(1/2),-(1/2),-(1/2),1/2}, {-(1/2),1/2,1/2,1/2}, {1/2,-(1/2),1/2,1/2}, <<9>>, {-(1/2),1/2,-(1/2),-(1/2)}, {1/2,-(1/2),-(1/2),-(1/2)}, {0,0,0,-1}}

3 added 403 characters in body
source | link

For the version of the question before Edit 2:

m = Range[0, 5];
a = -Range[15];
Pick[m, NonPositive[Max[# + a - 1] & /@ m]]
(* or Select[m, NonPositive[Max[# + a - 1] &]1]]&] *)

{0, 1, 2}

Update: For the general case, with M and A as in OP's Edit 2, simply change # + a -1 to #.Transpose[A] - 1:

Pick[M, NonPositive[Max[#.Transpose[A] - 1]& /@ M]]
(* or Select[M, NonPositive[Max[#.Transpose[A] - 1]]&] *)

{{0,0,0,1}, {-(1/2),-(1/2),-(1/2),1/2}, {-(1/2),1/2,1/2,1/2}, {1/2,-(1/2),1/2,1/2}, <<9>>, {-(1/2),1/2,-(1/2),-(1/2)}, {1/2,-(1/2),-(1/2),-(1/2)}, {0,0,0,-1}}

For the version of the question before Edit 2:

m = Range[0, 5];
a = -Range[15];
Pick[m, NonPositive[Max[# + a - 1] & /@ m]]
(* or Select[m, NonPositive[Max[# + a - 1] &] *)

{0, 1, 2}

For the version of the question before Edit 2:

m = Range[0, 5];
a = -Range[15];
Pick[m, NonPositive[Max[# + a - 1] & /@ m]]
(* or Select[m, NonPositive[Max[# + a - 1]]&] *)

{0, 1, 2}

Update: For the general case, with M and A as in OP's Edit 2, simply change # + a -1 to #.Transpose[A] - 1:

Pick[M, NonPositive[Max[#.Transpose[A] - 1]& /@ M]]
(* or Select[M, NonPositive[Max[#.Transpose[A] - 1]]&] *)

{{0,0,0,1}, {-(1/2),-(1/2),-(1/2),1/2}, {-(1/2),1/2,1/2,1/2}, {1/2,-(1/2),1/2,1/2}, <<9>>, {-(1/2),1/2,-(1/2),-(1/2)}, {1/2,-(1/2),-(1/2),-(1/2)}, {0,0,0,-1}}

2 added 50 characters in body
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    Post Undeleted by kglr
    Post Deleted by kglr
1
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