(Solved): please answer all parts of question Classify the origin as an attractor, repeller, or saddle point o ...

Classify the origin as an attractor, repeller, or saddle point of the dynamical system \( x_{k+1}=A_{k} \). Find the directions of greatest attraction and/or repulsion. \[ A=\left[\begin{array}{rr} -2.3 & 0.7 \\ -14.0 & 4.0 \end{array}\right] \] Classify the origin as an attractor, repeller, or saddle point. Choose the correct answer below A. The origin is an attractor B. The origin is a saddle point. C. The origin is a repeller Classify the origin as an attractor, repeller, or saddle point of the dynamical system \( x_{k+1}=A x_{k} \). Find the directions o greatest attraction and/or repulsion. \[ A=\left[\begin{array}{rr} -2.3 & 0.7 \\ -14.0 & 4.0 \end{array}\right] \] Find the direction of greatest attraction if it applies. Choose the correct answer below. A. The direction of greatest attraction is along the line through 0 and \( \left[\begin{array}{r}5 \\ 12\end{array}\right] \) B. The direction of greatest attraction is along the line through 0 and \( \left[\begin{array}{l}1 \\ 4\end{array}\right] \), c. The direction of greatest attraction is along the line through 0 and \( \left[\begin{array}{r}12 \\ 5\end{array}\right] \) D. The direction of greatest attraction is along the line through 0 and \( \left[\begin{array}{l}1 \\ 5\end{array}\right] \) E. The origin is a repeller it has no direction of greatest attraction Classify the origin as an attractor, repeller, or saddle point of the dynamical system \( x_{k+1}=A x_{k} \). Find the directions of greatest attraction and/or repulsion \[ A=\left[\begin{array}{rr} -2.3 & 0.7 \\ -14.0 & 4.0 \end{array}\right] \] E. The origin is a repeller. It has no direction of greatest attraction Find the direction of greatest repulsion if it applies Choose the correct answer below A. The direction of greatest repulsion is along the line through 0 and \( \left[\begin{array}{r}5 \\ 12\end{array}\right] \) B. The direction of greatest repulsion is along the line through 0 and \( \left[\begin{array}{l}1 \\ 4\end{array}\right] \) C. The direction of greatest repulsion is along the line through 0 and \( \left[\begin{array}{l}1 \\ 5\end{array}\right] \) D. The direction of greatest repulsion is along the line through 0 and \( \left[\begin{array}{c}12 \\ 5\end{array}\right] \) E. The ongin is an atfractor, it has no direction of greatest repulsion