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+//page 8
+//Example 1.5
+clear;
+close;
+clc;
+a = [2 -1 3 2; 1 4 0 -1; 2 6 -1 5];
+disp(a,'a=');
+disp('Applying row transformations:');
+disp('R1 = R1-2*R2');
+a(1,:) = a(1,:) - 2*a(2,:);
+disp(a,'a = ');
+disp('R3 = R3-2*R2');
+a(3,:) = a(3,:) - 2*a(2,:);
+disp(a,'a = ');
+disp('R3 = R3/-2');
+a(3,:) = -1/2*a(3,:);
+disp(a,'a = ');
+disp('R2 = R2-4*R3');
+a(2,:) = a(2,:) - 4*a(3,:);
+disp(a,'a = ');
+disp('R1 = R1+9*R3');
+a(1,:) = a(1,:) + 9*a(3,:);
+disp(a,'a = ');
+disp('R1 = R1*2/15');
+a(1,:) = a(1,:) * 2/15;
+disp(a,'a = ');
+disp('R2 = R2+2*R1');
+a(2,:) = a(2,:) + 2*a(1,:);
+disp(a,'a = ');
+disp('R3 = R3-R1/2');
+a(3,:) = a(3,:) - 1/2*a(1,:);
+disp(a,'a = ');
+disp('We get the system of equations as:');
+disp('2*x1 - x2 + 3*x3 + 2*x4 = 0');
+disp('x1 + 4*x2 - x4 = 0');
+disp('2*x1 + 6* x2 - x3 + 5*x4 = 0');
+disp('and');
+disp('x2 - 5/3*x4 = 0','x1 + 17/3*x4 = 0','x3 - 11/3*x4 = 0');
+disp('now by assigning any rational value c to x4 in system second, the solution is evaluated as:');
+disp('(-17/3*c,5/3,11/3*c,c)');
+//end