- #1
Ackbach
Gold Member
MHB
- 4,155
- 91
Here's this week's problem.
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Diagonalize the matrix
$$A=\begin{bmatrix}
0 &1 &0 \\
0 &0 &1 \\
30 &1 &-6
\end{bmatrix}.$$
Note that this procedure can be used to compute $e^{At}$, and thus
solve the system of ODE's $x'=Ax$, the solution being $e^{At}x_{0}$.
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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
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Diagonalize the matrix
$$A=\begin{bmatrix}
0 &1 &0 \\
0 &0 &1 \\
30 &1 &-6
\end{bmatrix}.$$
Note that this procedure can be used to compute $e^{At}$, and thus
solve the system of ODE's $x'=Ax$, the solution being $e^{At}x_{0}$.
-----
Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!