Question

Consider the transformation T:x=4041u−941v, y=941u+4041v A. Compute the Jacobian: ∂(x,y)∂(u,v)= B. The transformation is linear, which implies that it transforms lines into lines. Thus, it transforms the square S:−41≤u≤41,−41≤v≤41 into a square T(S) with vertices: T(41, 41).

Answer 1

A. The Jacobian for the transformation

$\begin{cases}x=\dfrac{40}{41}u-\dfrac9{41}v\\\\y=\dfrac9{41}u+\dfrac{40}{41}v\end{cases}$

is

$\dfrac{\partial(x,y)}{\partial(u,v)}=\begin{bmatrix}\dfrac{\partial x}{\partial u}&\dfrac{\partial x}{\partial v}\\\\\dfrac{\partial y}{\partial u}&\dfrac{\partial y}{\partial v}\end{bmatrix}=\begin{bmatrix}\dfrac{40}{41}&-\dfrac9{41}\\\\\dfrac9{41}&\dfrac{40}{41}\end{bmatrix}$

B. This question seems to be incomplete...