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+//page 37

+//Example 2.8

+clear;

+clc;

+close;

+a1 = [1 2 0 3 0];

+a2 =[0 0 1 4 0];

+a3 = [0 0 0 0 1];

+disp(a1,'a1 = ');

+disp(a2,'a2 = ');

+disp(a3,'a3 = ');

+disp('By theorem 3, vector a is in subspace W of F^5 spanned by a1, a2, a3');

+disp('if and only if there exist scalars c1, c2, c3 such that');

+disp('a= c1a1 + c2a2 + c3a3');

+disp('So, a = (c1,2*c1,c2,3c1+4c2,c3)');

+c1 = -3;

+c2 = 1;

+c3 = 2;

+a = c1*a1 + c2*a2 + c3*a3;

+disp(c1,'c1 = ');

+disp(c2,'c2 = ');

+disp(c3,'c3 = ');

+disp(a,'Therefore, a = ');

+disp('This shows, a is in W');

+disp('And (2,4,6,7,8) is not in W as there is no value of c1 c2 c3 that satisfies the equation');

+//end