Laplace Transform to Solve a Diff. Eq. System spent hours on this one =*(

jjtx300
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Homework Statement


[PLAIN]http://img710.imageshack.us/img710/3381/38442384.jpg

The Attempt at a Solution


[PLAIN]http://img695.imageshack.us/img695/6295/56987528.jpg

Thanks in advance,
JJ
 
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Shouldn't you have s\textbf{I}-\textbf{A}=\begin{pmatrix}s+3 & -4 \\ 2 & s-3\end{pmatrix}[/itex] in your first step?
 
oh my gosh... yes that's exactly what I did wrong. Thank you sooooooo much! It's amazing how some silly mistakes can just stop you in your tracks and drive you crazy some times.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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