Let $A = \left( \begin{array} { c c }
- 1 & - 4 \
1 & - 1
\end{array} \right)$ , and consider the system $X ^ { \prime } = A X$ . The critical point $( 0,0 )$ of the system is a spiral point. The origin is
A) unstable, and the solutions recede from the origin clockwise as $t \rightarrow \infty$ .
B) unstable, and the solutions recede from the origin counter-clockwise as $t \rightarrow \infty$ .
C) stable, and the solutions approach the origin clockwise as $t \rightarrow \infty$ .
D) stable, and the solutions approach the origin counter-clockwise as $t \rightarrow \infty$ .
E) none of the above

Question

Let $A = \left( \begin{array} { c c } 
- 1 & - 4 \
1 & - 1
\end{array} \right)$ , and consider the system $X ^ { \prime } = A X$ . The critical point $( 0,0 )$ of the system is a spiral point. The origin is
A) unstable, and the solutions recede from the origin clockwise as $t \rightarrow \infty$ .
B) unstable, and the solutions recede from the origin counter-clockwise as $t \rightarrow \infty$ .
C) stable, and the solutions approach the origin clockwise as $t \rightarrow \infty$ .
D) stable, and the solutions approach the origin counter-clockwise as $t \rightarrow \infty$ .
E) none of the above

Quizplus · Accepted Answer

The Answer of Let $A = \left( \begin{array} { c c } 
- 1 & - 4 \
1 & - 1
\end{array} \right)$ , and consider the system $X ^ { \prime } = A X$ . The critical point $( 0,0 )$ of the system is a spiral point. The origin is
A) unstable, and the solutions recede from the origin clockwise as $t \rightarrow \infty$ .
B) unstable, and the solutions recede from the origin counter-clockwise as $t \rightarrow \infty$ .
C) stable, and the solutions approach the origin clockwise as $t \rightarrow \infty$ .
D) stable, and the solutions approach the origin counter-clockwise as $t \rightarrow \infty$ .
E) none of the above

Let A=(−1−41−1)A = \left( \begin{array} { c c } - 1 & - 4 \\1 & - 1\end{array} \right)A=(−11​−4−1​)

Let $A = \left( \begin{array} { c c } - 1 & - 4 \\1 & - 1\end{array} \right)$