Is T a Linear Mapping from R2 to R1?

[affans]

Homework Statement

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

Homework Equations

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]

Homework Statement

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

Homework Equations

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.)