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+//Eg-3.5
+//pg-78
+
+clear
+clc
+
+ // Matrices A and B (AX=B)  
+ A=[-4 1 0 0 0 1;3 -7 2 0 2 0;0 4 -7 3 0 0;0 0 1 -5 4 0;0 2 0 6 -11 3;3 0 0 0 3 -8];
+ [n,n]=size(A);
+ B=[-130;0;0;0;0;0];
+ 
+ //Initialising Permutation matrix(which keeps note of column changes in this code) as Identity matrix
+ P=eye(n);
+ 
+ //Algorithm of gauss elimination with complete pivoting
+ 
+ //COMPLETE PIVOTING(both rows and columns)
+ //loop from 1 to n-1 pivot elements
+   for k=1:n-1
+        u=k;
+        l=k;
+        big=abs(A(k,k)); 
+ //Obtaining max absolute element and its position/index in column        
+        for t=k+1:n      
+        dummy=abs(A(t,k));
+        if dummy>big
+            big=dummy;
+            u=t;
+        end
+    end
+ //Obtaining max absolute element and its position/index in row
+        for t=k+1:n
+            dummy=abs(A(k,t));
+            if dummy>big
+                big=dummy;
+                l=t;
+    end
+end
+//Row and Column interchanges according to index of maximum absolute element obtained
+    if l~=k
+        for j=1:n//column interchanges
+            dummy=A(j,l);
+            A(j,l)=A(j,k);
+            A(j,k)=dummy;
+            temp=P(j,l);//column interchanges are noted with the help of a permutation matrix
+            P(j,l)=P(j,k);
+            P(j,k)=temp;
+        end
+    elseif u~=k
+        for j=1:n//row interchanges
+            dummy=A(u,j);
+            A(u,j)=A(k,j);
+            A(k,j)=dummy;
+        end
+            temp=B(u);//B rows are also interchanged according to A row interchanges
+            B(u)=B(k);
+            B(k)=temp;
+        end
+        
+//Forward Elimination
+        for i=(k+1):n
+            facotr=A(i,k)/A(k,k);
+            for j=1:n
+                A(i,j)=A(i,j)-facotr*A(k,j);
+            end
+            B(i)=B(i)-facotr*B(k);
+        end
+    end  
+      
+ //Backward Substitution
+    X=zeros(n,1);
+    X(n)=B(n)/A(n,n);
+    for i=(n-1):-1:1
+        summ=B(i);
+        for j=(i+1):n
+            summ=summ-A(i,j)*X(j);
+        end
+              X(i)=summ/A(i,i);
+    end
+ //Column interchanges in A correspond to row interchanges in X which can be cancelled out by multiplying with the permutation matrix defined above 
+    X=P*X;
+    
+ //Result
+ v1=X(1);
+ v2=X(2);
+ v3=X(3);
+ v4=X(4);
+ v5=X(5);
+ v6=X(6);
+ 
+ //Displaying Results
+ disp(v1,"v1=")
+ disp(v2,"v2=")
+ disp(v3,"v3=")
+ disp(v4,"v4=")
+ disp(v5,"v5=")
+ disp(v6,"v6=")
+   
+\ No newline at end of file