where A is a $2 \times$ 2 matrix.
1. 1. Write down matrix A .
A=$ \begin{Bmatrix} a & b \\ c & d \end{Bmatrix} $
a= ,b= ,c= ,d= .
2. Find the eigenvalues and corresponding eigenvectors of matrix A .
2. Hence write down the general solution of the system.
$X$=A e$^{-t}$$ \begin{Bmatrix} a \\ -1 \end{Bmatrix} $+B $e^{4 t}$$\begin{Bmatrix} b \\ 2 \end{Bmatrix} $
a= ,b= .
3. Determine whether the equilibrium point E(0,0) is stable or unstable. Justify your answer.
4. Find the value of $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at point:
1. $ \mathrm{P}(5,0) $ is .
2. $ \mathrm{Q}(-5,0)$ is .
5. Sketch a phase portrait for the general solution to the system of coupled diff erential equations for $-8 \leq x \leq 8$ and $-8 \leq y \leq 8$ .
