The function T: R2 -> R1 defined by T(x,y) = (y^2)x + (x^2)y is not a linear mapping. A function is considered linear if it satisfies two conditions: f(ax) = a f(x) and f(x+y) = f(x) + f(y) for all vectors x, y in the domain. The discussion highlights a misunderstanding regarding the mapping of points, clarifying that a single point in R2 maps to a single point in R1, which does not imply linearity.
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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 what said.)affans said: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.