GRAM-SCHMIDT

VSet:={MatrixForm[Transpose[v1]], MatrixForm[Transpose[v2]],MatrixForm[Transpose[v3]],MatrixForm[Transpose[v4]],MatrixForm[Transpose[v5]]}

f[a_,b_]:=If[ {a.Transpose[a]}[[1]][[1]][[1]]==0,0,(({a.Transpose[b]}[[1]][[1]][[1]])/({a.Transpose[a]}[[1]][[1]][[1]]))a]

u1:=v1;
u2:=v2-f[u1,v2]
u3:=v3-f[u1,v3]-f[u2,v3]
u4:=v4-f[u1,v4]-f[u2,v4]-f[u3,v4]
u5:=v5-f[u1,v5]-f[u2,v5]-f[u3,v5]-f[u4,v5]


GS:={MatrixForm[Transpose[u1]],MatrixForm[Transpose[u2]],MatrixForm[Transpose[u3]],MatrixForm[Transpose[u4]],MatrixForm[Transpose[u5]]}

(* INSERT THE VECTORS *)
v1:={{1,2,3,0}}
v2:={{2,3,4,0}}
v3:={{3,4,5,0}}
v4:={{0,3,4,5}}
v5:={{0,0,0,0}}

"VECTORS SET"
VSet
"GRAM-SCHMIDT"
GS

(* INSERT THE VECTORS *)
v1:={{1,2,3,0}}
v2:={{2,3,4,0}}
v3:={{3,4,5,0}}
v4:={{0,3,4,5}}
v5:={{2,1,1,1}}

"VECTORS SET"
VSet
"GRAM-SCHMIDT"
GS

(* INSERT THE VECTORS *)
v1:={{1,2,3,0}}
v2:={{2,2,4,0}}
v3:={{3,4,5,0}}
v4:={{0,3,4,5}}
v5:={{2,1,1,1}}

"VECTORS SET"
VSet
"GRAM-SCHMIDT"
GS