Math Help - ELA Question: Transformation

1. ELA Question: Transformation

Here is the question:

2. Originally Posted by Phyxius117
Here is the question:

I am assumeing they want this with respect to the standard basis!

With that said

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

Then

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

This first equality holds by the Linearity of T

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

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

Now we have a system of equations for

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

These are the columns of the matrix.

3. Thank You!!!