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Left_Null_and_Column_Space.m
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% Matrix_awal
% A= [1 2 1 1 5
% -2 -4 0 4 -2
% 1 2 2 4 9 ]
A=[1 -2 1; 2 -4 2; 1 0 2; 1 4 4; 5 -2 9];
% A=[1 2 4; 0 0 0; 0 3 6];
BB=A;
B=5; K=3;
% B=3; K=3;
for D=1 : K
for E=1 : B
if A(1,1)~=0
if(D+E)<=B
if A((D+E),D)~=0
r= A((D+E),D)/A(D,D);
if A(D,D)~=0
for Z=1:K
A((D+E),Z)=A((D+E),Z)-(r*A(D,Z));
end
else
for Z=1:K
A((D+E),Z)=A((D+E),Z);
end
end
else
C=1;
while A((D+E),(D+C))~=0
for C= 1 : (K-D)
r= A((D+E),(D+C))/A((D),(D+C));
for Z=1:K
A((D+E),Z)=A((D+E),Z)-(r*A(D,Z));
end
end
end
end
end
end
end
end
%----------------------------- Penentuan nilai rank-----------------------
counter=0;
Inverse_rank=0;
for U=1: B
for L=1 : K
if A(U,L) == 0
counter=counter+1;
end
end
if (counter/K)==1
Inverse_rank=Inverse_rank+1;
end
counter=0;
end
rank=B-Inverse_rank;
%----------------------------- Penentuan column space ------------------
BE=zeros(rank,K);
counter1=0;
UU=0;
for U1=1: B
for L1=1 : K
if A(U1,L1) ~= 0
counter1=counter1+1;
end
end
if ((counter1)/K) > 0.00
UU=UU+1;
for Z= 1 : K
BE(UU,Z)=BB(U1,Z);
end
end
counter1=0;
end
Basic=BE';
Column_Space=Basic;
Matrix_Baru=A;
%----------------------- Left Null Space------------------
counter3=0;
for U2 = 1 : B
for L2 = 1 : K
if (Matrix_Baru(U2,L2)~= 0)
counter3=counter3+1;
if (counter3/1) == 1
if (Matrix_Baru(U2,L2)~= 1)
OKE=Matrix_Baru(U2,L2);
for ZZ= 0 : (K-L2)
Matrix_Baru(U2,L2+ZZ)= Matrix_Baru(U2,L2+ZZ)/ OKE;
end
end
if (L2+1)<= K
for ZE= L2 : K
if (ZE+1) <= K
Matrix_Baru(U2,ZE+1)=-1*Matrix_Baru(U2,ZE+1);
end
end
end
end
end
end
counter3=0;
end
%OKE1=0;
counter3=0;
for U2 = 1 : K
for L2 = 1 : B
if (Matrix_Baru(L2,U2)~= 0)
counter3=counter3+1;
end
if (counter3)==2
counter1=counter1+1;
if counter1==1
for UU=1:K
if (U2+UU)<=K
Matrix_Baru(1,(U2+UU))=(Matrix_Baru(1,U2)*Matrix_Baru(L2,(U2+UU)))+(Matrix_Baru(1,(U2+UU)));
end
end
Matrix_Baru(1,U2)=0;
end
end
end
counter3=0;
end
%--------------------------------------------Done---------------------------------------------
counter1=0;
Matrix_Baru1=Matrix_Baru;
Baru=zeros(K,K);
for T = 1 : B
for Y = 1 : K
if Matrix_Baru1(T,Y) ~= 0
counter1=counter1+1;
end
if (counter1/1==1)
for zx=1 : K
if (zx+Y)<= K
if Matrix_Baru1(T,(Y+zx))~=0
Baru(Y,(Y+zx))=Matrix_Baru1(T,(Y+zx));
end
end
end
end
end
counter1=0;
end
counterx=0;
for T = 1 : K
for Y = 1 : K
if(Baru(T,Y))~=0
counter1=counter1+1;
if(counter1==1)
for T = 1 : K
for Y = 1 : K
if Baru(Y,T) ~= 0
counterx=counterx+1;
if counterx ~= 0
Baru(T,T)=1;
end
end
end
counterx=0;
end
end
end
end
counter1=0;
end
counter2=0;
Baru1=Baru;
for O = 1 : K
for P = 1 : K
if ((O-counter2))>0
if (Baru1(P,O-counter2)) == 0
counter1=counter1+1;
end
if (counter1==K)
counter2=counter2+1;
Baru1(:,((O-counter2)+1))=[];
end
end
end
counter1=0;
end
Left_Null_Space=Baru1
Column_Space