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+//example no. 3.12
+//solve system by decomposition method
+
+A=[1 1 -1;2 2 5;3 2 -3]
+
+b=[2;-3;6]
+
+
+
+       // hence we can observe that LU decomposition method fails to solve this system since the pivot L(2,2)=0;
+       
+       
+       //we note that the coefficient matrix is not a positive definite matrix and hence its LU decomposition is not guaranteed,
+       
+       
+       //if we interchange the rows of A as shown below the LU decomposition would work,
+       
+       A=[3 2 -3;2 2 5;1 1 -1]
+       
+       b=[6;-3;2]
+       
+       [U,L]=LandU(A,3)        // call LandU function to evaluate U,L of A,
+
+n=3;
+Z=fore(L,b);
+
+X=back(U,Z)
+                 
+\ No newline at end of file