Question

If u=x(1-y) and v=xy, then find the value of the Jacobian ∂u,v∂(x,y)

Select one:

A -x

B x2

C -x2

D x

Answer 1

$\frac{\partial \left( u,v \right)}{\partial \left( x,y \right)}=\left| \begin{matrix} \frac{\partial u}{\partial x}& \frac{\partial v}{\partial x}\\ \frac{\partial u}{\partial y}& \frac{\partial u}{\partial y}\\\end{matrix} \right|=\left| \begin{matrix} 1-y& y\\ -x& x\\\end{matrix} \right|=x\left( 1-y \right) +xy=x$