Jacobian Matrix and Jacobian - Maple Programming Help

Jacobian Matrix and Jacobian

 Description Calculate the Jacobian matrix and Jacobian of a set of multivariate functions.

Jacobian Matrix and Jacobian

Functions

 >
 ${{x}}^{{2}}{+}{y}{}{z}{,}{2}{-}{x}{}{y}{,}{{y}}^{{2}}{-}{z}$ (1)

Variables

 > ${x}{,}{y}{,}{z}$
 ${x}{,}{y}{,}{z}$ (2)

Point P

 > $\left[{1}{,}{2}{,}{a}\right]$
 $\left[{1}{,}{2}{,}{a}\right]$ (3)

Jacobian Matrix

 > $\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{Jacobian}\right]\left(\left[\right],\left[\right]\right)$
 $\left[\begin{array}{ccc}{2}{}{x}& {z}& {y}\\ {-}{y}& {-}{x}& {0}\\ {0}& {2}{}{y}& {-}{1}\end{array}\right]$ (4)

Jacobian Matrix at P

 > $\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{Jacobian}\right]\left(\left[\right],\left[\right]=\right)$
 $\left[\begin{array}{ccc}{2}& {a}& {2}\\ {-}{2}& {-}{1}& {0}\\ {0}& {4}& {-}{1}\end{array}\right]$ (5)

Jacobian

 > $\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{Jacobian}\right]\left(\left[\right],\left[\right],\mathrm{output}=\mathrm{determinant}\right)$
 ${2}{}{{x}}^{{2}}{-}{2}{}{{y}}^{{3}}{-}{y}{}{z}$ (6)

Jacobian at P

 > $\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{Jacobian}\right]\left(\left[\right],\left[\right]=,\mathrm{output}=\mathrm{determinant}\right)$
 ${-}{14}{-}{2}{}{a}$ (7)

 Commands Used