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Linear mapping.

  • Thread starter affans
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  • #1
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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.
 

Answers and Replies

  • #2
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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
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
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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.)
 

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