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## Homework Statement

Determine if the following T is linear tranformation, and give the domain and range of T:

T(x,y) = (x + y

^{2}, [tex]\sqrt[3]{xy}[/tex] )

## Homework Equations

T (

**u**+

**v**) = T(

**u**) + T(

**v**)

T(r

**u**) = rT(

**u**)

## The Attempt at a Solution

1)

let

**u**= (x1, x2);

T(r

**u**) = T(rx1, rx2)

T(r

**u**)= r(x + y

^{2}) , r([tex]\sqrt[3]{xy}[/tex] )

T(r

**u**) = r(x + y

^{2}, [tex]\sqrt[3]{xy}[/tex] )

so it suffices the first condition, right?

2)

let

**u**= (x1, y1) and let

**v**= (y1, y2);

T (

**u**+

**v**) = T ( x1 + y1, x2 + y2)

T (

**u**+

**v**) = Here I am confused with the term ( x + y

^{2})

T (

**u**+

**v**)

Any help please !