1.4.2 y(r) = Mar(1- r|,0) %3D to show this function is not a positive definite function we use definition 1 and set n = 3 we have 72 3 | i=l j=1 i=l j=l GĞMar(1 – |r1 – r1|.0) + c&Mar(1 – |n - 2).0)...

Solve and find x's and c's such that answer will be less than zero

Extracted text: 1.4.2 y(r) = Mar(1- r|,0) %3D to show this function is not a positive definite function we use definition 1 and set n = 3 we have 72 3 | i=l j=1 i=l j=l GĞMar(1 – |r1 – r1|.0) + c&Mar(1 – |n - 2).0) %! + cĞMar(1 – h - r3l .0) I3/,0) (o || + xÃMar(1 – |e2 - 21|.0) + cx5Mar(1= |22-12|.0) – |r2 - z3|,0) + Cxci Mar(1 –|r3- z1|,0) + CsMar(1- |23 – 12|,0) + Ca¢zMar(1– |r3 – 13|,0) + xgMar(1 Now we take common factors