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+//page 70

+//Example 3.6

+clc;

+clear;

+close;

+a1 = [1 2];

+a2 = [3 4];

+disp(a1,'a1 = ');

+disp(a2,'a2 = ');

+disp('a1 and a2 are linearly independent and hence form a basis for R^2');

+disp('According to theorem 1, there is a linear transformation from R^2 to R^3 with the transformation functions as:');

+Ta1 = [3 2 1];

+Ta2 = [6 5 4];

+disp(Ta1,'Ta1 = ');

+disp(Ta2,'Ta2 = ');

+disp('Now, we find scalars c1 and c2 for that we know T(c1a1 + c2a2) = c1(Ta1) + c2(Ta2))');

+disp('if(1,0) = c1(1,2) + c2(3,4), then ');

+c = inv([a1;a2]') * [1;0];

+c1 = c(1,1);

+c2 = c(2,1);

+disp(c1,'c1 = ');

+disp(c2,'c2 = ');

+disp('The transformation function T(1,0) will be:');

+T = c1*Ta1 + c2*Ta2;

+disp(T,'T(1,0) = ');

+//end