The Jacobian Matrix of the System $x ^ { \prime } = x ^ { 3 } - y ^ { 2 } + 4 , y ^ { \prime } = 5 x$

Multiple Choice

The Jacobian matrix of the system $x ^ { \prime } = x ^ { 3 } - y ^ { 2 } + 4 , y ^ { \prime } = 5 x$ at the critical point $( 0 , - 2 )$

A) $A = \left[ \begin{array} { c c } 0 & - 4 \\5 & 0\end{array} \right]$
B) $A = \left[ \begin{array} { l l } 0 & 4 \\5 & 0\end{array} \right]$
C) $A = \left[ \begin{array} { r r } 3 x ^ { 2 } & 2 y \\5 & 0\end{array} \right]$
D) $A = \left[ \begin{array} { r r } 3 x ^ { 2 } & - 2 y \\5 & 0\end{array} \right]$
E) $A = \left[ \begin{array} { r r } 3 x ^ { 2 } & - 2 y \\0 & 5\end{array} \right]$