Consider the Non-Linear System $x ^ { \prime } = 1 - 2 x y , y ^ { \prime } = 2 x y - y$

Multiple Choice

Consider the non-linear system $x ^ { \prime } = 1 - 2 x y , y ^ { \prime } = 2 x y - y$ . The linearized system about the one critical point, $( 1 / 2,1 ) \text {, is } X ^ { t } = A X \text {, where } A =$

A) $\left( \begin{array} { l l } 2 & 1 \\2 & 0\end{array} \right)$
B) $\left( \begin{array} { c c } 2 & - 1 \\2 & 0\end{array} \right)$
C) $\left( \begin{array} { c c } - 2 & - 1 \\2 & 0\end{array} \right)$
D) $\left( \begin{array} { l l } - 2 & 1 \\- 2 & 0\end{array} \right)$
E) $\left( \begin{array} { c c } - 2 & - 1 \\- 2 & 0\end{array} \right)$