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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