00:01
Let's solve this question, dy divided by dt is equals to minus 2 minus 3, 3 minus 2 y.
00:09
For finding the eigenvalues we need to calculate that mod of a minus lambda i is equals to 0.
00:17
So that implies that we can write minus 2 minus lambda minus 3, 3 minus 2 minus lambda is equals to 0.
00:27
That implies that minus 2 minus lambda whole square plus 9 is equals to 0.
00:33
That gives lambda square plus 4 lambda plus 13 is equals to 0.
00:41
So that for lambda is equals to minus 4 plus or minus square root of 16 minus 52 divided by 22.
00:49
So that is equals to we will get minus 4 plus or minus 6 i divided by, for eigenvalues that is lambda 1 is equals to minus 2 plus 3 i and lambda 2 that is minus 2 minus 3 i.
01:04
Now at lambda 1 is equals to minus 2 plus 3 i, the eigenvectors that will be here minus 2 plus 2 minus 3 i minus 3, 3 minus 2 plus 2 minus 3 i.
01:18
Here it is v1 v2 is equals to 0.
01:23
So therefore that implies that minus 3 i v1 minus 3 v2 is equals to 0.
01:31
Minus 3 i v1 is equals to 3 v2.
01:34
So that implies that v1 divided by v2 is equals to 3 divided by minus 3 i is equals to minus 1 divided by i is equals to i...