# help with linear systems

• April 3rd 2011, 12:28 AM
twostep08
help with linear systems
i have a midterm on all this stuff on monday. the professor posted a practice exam without solutions, and i cant seem to remember how to do the first 2 problems.. id be soooooooooooooooooo appreciative if someone can walk me through them. heres the link to them, as im sure itll be easier to read than me posting them here.

http://www.math.uconn.edu/~mckenna/2410f09/exam209f.pdf
• April 3rd 2011, 12:39 AM
FernandoRevilla
The problem is just routine knowing the corresponding theory. At any case, some hints:

$(a)\quad Y(t)=e^{tA}\begin{bmatrix}{c_1}\\{c_2}\end{bmatrix }=\ldots$

$(b)\quad A$ has a positive and a negative eigenvalue.

$(c)\quad Y(t)=e^{tA}\begin{bmatrix}{\;\;1}\\{-1}\end{bmatrix}=\ldots$