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) $\left( \begin{array} { c c }
- 2 & - 1 \
- 2 & 0
\end{array} \right)$

Question

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) $\left( \begin{array} { c c } 
- 2 & - 1 \
- 2 & 0
\end{array} \right)$

Quizplus · Accepted Answer

The Jacobian matrix of the system at the critical point $(1/2, 1)$ is $\left( \begin{array}{cc} -2 & -1 \ 2 & 0 \end{array} \right)$.

Consider the Non-Linear System x′=1−2xy,y′=2xy−yx ^ { \prime } = 1 - 2 x y , y ^ { \prime } = 2 x y - yx′=1−2xy,y′=2xy−y

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