- #1
ythamsten
- 16
- 0
Homework Statement
Let T:R2→R2 be the linear transformation such that T(x,y)→(9x+3y,5x+2y). Let R be the region on the plane defined as {(x,y) [itex]\in[/itex] R2/ 0≤x≤2 and 0≤y≤2 }. Consider the region T(R) [itex]\subset[/itex] R2, which is the image of the region R by the linear transform T. What is the area of the region T(R)?
PS: When I write purely R, I refer to the region. And when I write R2, to the plane. Just to make it clear
Homework Equations
N/A
The Attempt at a Solution
Well, I'm not making quite progress. I mean, I've notice some things, e.g. this linear transformation is a linear operator, that it is also surjective (it's image covers the whole plane). To begin with, I think the region R is like a little square, with area 4. But I get quite confused afterwards on what T(R) really looks like and then in computing it. Hope for some help, thanks in advance.