Linear mapping.

[affans]

1. The problem statement, all variables and given/known data

Let T: R2 -> R1 be given by T(x,y) = (y^2)x + (x^2)y.
Is T linear? justify your answer


2. Relevant equations


3. The attempt at a solution

Yes it is a linear mapping because both points map onto one point.

[waht]

a function f(x) is linear if

f(ax) = a f(x) ; where "a" is some constant

and f(x+y) = f(x) + f(y)

see if your function satisfies these

[HallsofIvy]

1. The problem statement, all variables and given/known data

Let T: R2 -> R1 be given by T(x,y) = (y^2)x + (x^2)y.
Is T linear? justify your answer


2. Relevant equations


3. The attempt at a solution

Yes it is a linear mapping because both points map onto one point.
This is very distressing. Just about everything you say here is wrong. There are not two points being mapped to one. The single point (x,y) in R2 is mapped to a single point in R1. But, in any case, that has NOTHING to do with being "linear". Please review the definition of "linear mapping". (It is basically what waht said.)