MAT 343 EXAM 3
(due Tue. next week in class)

NAME:______________________

ASU ID:_____________________

1. Find the general solutions for the linear systems of the form

$$\dot x = M x$$

where $M$ takes the matrix values $A,\;\;B,\;\;C$ defined as follows.

$$A=\left( \begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 1 \\ ... ... & 0 & 0 & 0 & 1\\ -8 & 0 & 0 & -9 & 0 & 0 \end{array}\right)$$

2. Classify the following second order curves and sketch them in the original coordinate system $(x,y).$

$$x^2 + 4 xy + 4 y^2 + 4x + 4 =0$$

$$x^2 +2\sqrt{3}xy - y^2 + 2x -1 = 0$$

$$3x^2 -2\sqrt{3}xy + 5y^2 + x +y = 0$$