00:01
In this problem, we are going to solve the following system.
00:05
Dx over dt equal to 2, 12, minus 2, minus 8, times x with the initial condition x0 equal to 0, 5.
00:19
Let's call this a.
00:21
This is the mixing matrix.
00:24
And now we are going to diagonalize a.
00:27
So determinant a minus lambda equal to 0.
00:32
So we first find the eigenvalues.
00:36
And here we have determinant 2 minus lambda, 12 minus 2 minus 8 minus lambda.
00:45
And this is equal to lambda squared plus 6 lambda plus 8.
00:53
So the solutions are or the eigenvalues are minus 4 and minus 2.
01:00
Now let us obtain eigenvectors.
01:02
So 4 lambda equal to minus 4.
01:07
Here the following.
01:08
Let's call this eigenvector ab...