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+//Eg-3.7
+//pg-86
+
+clear
+clc
+
+ //Matrices A and B
+ A=[-0.41 0.58 1 0 0;0.41 0.58 0 1 0;-.82 -.58 0 0 1;.82 .58 0 0 0;-.82 .58 0 0 0];;
+ B=[0;3;0;6.25;0];
+[n,n]=size(A);
+
+//Permutation,Lower triangular matrix initialisation
+P=eye(n);
+L=zeros(n,n);
+
+//Algorithm of LU decomposition to find L,U,P and X
+//Partial Pivoting 
+   for k=1:n-1
+        u=k;
+        big=abs(A(k,k));
+        for t=k+1:n
+        dummy=abs(A(t,k));
+        if dummy>big//Finidng max absolute element
+            big=dummy;
+            u=t;//Index of max ansolute element
+        end
+    end
+        if u~=k
+        for j=1:n
+            dummy=A(u,j);//Interchanging rows of A
+            A(u,j)=A(k,j);
+            A(k,j)=dummy;
+
+            dummy=L(u,j);//interchanging rows of lowertriangular matrix according to A
+            L(u,j)=L(k,j);
+            L(k,j)=dummy;
+            end
+            dummy=B(u);//interchanging rows of B matrix
+            B(u)=B(k);
+            B(k)=dummy;
+        end
+    
+ //forward elimination to get U and sending corresponding factors to L   
+    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);
+                U=A;//upper triangular matrix
+            end
+            for j=k
+                L(i,j)=facotr;//factors are transformed to lower triangular matrix
+            end
+            
+        end 
+    end
+    
+ //Lower triangular matrix   
+    for s=1:n
+            L(s,s)=1;
+        end
+        
+ //Initialisation of D,X       
+     D=zeros(n,1);
+     X=zeros(n,1);
+     
+ //Forward Substitution Ld=B..we get d here
+      D(1)=B(1)/L(1,1);
+                 for i=2:n
+        summ=B(i);
+        for j=1:i-1
+            summ=summ-L(i,j)*D(j);
+        end
+        D(i)=summ/L(i,i);
+    end
+    
+ //Backward substitution  Ux=B gives X
+         X(n)=D(n)/U(n,n);
+    for i=(n-1):-1:1
+        summ=D(i);
+        for j=(i+1):n
+            summ=summ-U(i,j)*X(j);
+        end
+        X(i)=summ/U(i,i);
+    end
+    
+//Displaying results
+disp(X(1),"F0=")
+disp(X(2),"F1=")
+disp(X(3),"F2=")
+disp(X(4),"F3=")
+disp(X(5),"F4=")
+    
+    
+\ No newline at end of file