# Math Help - Linear Transformation

1. ## Linear Transformation

Please anyone help me to Determine the matrix $[T: B_1, B_2]$ for the given Linear Transformation $T:V_2 \to V_2 , T(x,y)=(x,-y)$ and the basis $B_1 = \{(1,1),(1,0)\}$ and $B_2 = \{(2,3),(4,5)\}$.

Thanks..

2. ## Re: Linear Transformation

Express:

$\begin{Bmatrix} T(1,1)=(1,-1)=a(2,3)+b(4,5)\\ T(1,0)=(1,0)=c(2,3)+d(4,5) \end{matrix}$

Then, $[T:\;B_1,B_2]=\begin{bmatrix}{a}&{c}\\{b}&{d}\end{bmatrix}$

So, you only need to solve two systems.

3. ## Re: Linear Transformation

It is so useful hint...
Thanks..