Here is the question:

http://i10.photobucket.com/albums/a1...7/problem3.png

Help please thanks!

Printable View

- Sep 30th 2010, 10:32 AMPhyxius117ELA Question: Transformation
Here is the question:

http://i10.photobucket.com/albums/a1...7/problem3.png

Help please thanks! - Sep 30th 2010, 11:01 AMTheEmptySet
I am assumeing they want this with respect to the standard basis!

With that said

let $\displaystyle e_1=(1,0)$ and $\displaystyle e_2=(0,1)$

Then

$\displaystyle (2,-2)=2e_1-2e_2 \iff T(2e_1-2e_2) =2T(e_1)-2T(e_2) = 16e_1+4e_2$

This first equality holds by the Linearity of T

Now we do the same this for the 2nd vector to get

$\displaystyle T(-4e_1-3e_2)=-4T(e_1)-3T(e_2)=-39e_1-36e_2$

Now we have a system of equations for

$\displaystyle T(e_1) \text{ and } T(e_2)$

These are the columns of the matrix. - Sep 30th 2010, 12:05 PMPhyxius117
Thank You!!!