Question

Find the absolute value of the jacobian, ∣∣∂(x,y)∂(s,t)∣∣, for the change of variables given by x=s+5t,y=3s+8t

Answer 1

`\left\|(\partial(x,y))/(\partial(s,t))\right\|=\left|\begin{vmatrix}(\partial x)/(\partial s)&(\partial x)/(\partial t)\\\\(\partial y)/(\partial s)&(\partial y)/(\partial t)\end{vmatrix}\right|=\left|\begin{vmatrix}1&5\\3&8\end{vmatrix}\right|=|-7|=7`