DSE 1008-Linear function

[kangkan]

Please help with the logic of question 16- DSE 2008

Thanks

[Dreyfus]

A function f(x) {where x is 2dimensional vector as given in the question} is linear transformation if two conditions are satisfied:
Condition 1 : f(a+b) = f(a) + f(b) where a nd b are both 2 dimensional vectors
Condition 2 : f(c*a) = c*f(a) where c is scalar
Since f(x1, x2) is not satisfying condition 1 therefore it is not a linear function but g(x1,y1) is satisfying both the conditions therefore its a linear function