00:01
In this question, we are given a matrix a is equal to minus 5, 1, 4, minus 2.
00:11
In the first subpart, we need to obtain the eigenvalues of this vector.
00:22
For obtaining the eigenvalue, the determinant a minus lambda i would be created to 0.
00:29
Substituting the values, we get negative 5, 1, 4, negative 2 minus lambda times identity metrics, that is 1 0 ,0, 1.
00:43
And the determinant of this whole matrix is repeated to 0.
00:47
Solving this we get negative 5 minus lambda 1, so negative of 2 minus lambda, determinant is equal to 0.
01:01
That is negative 5 minus lambda times negative 2 minus lambda minus lambda minus 4 is equal to 0.
01:11
10 plus 7 lambda plus lambda square minus 4 is equal to 0.
01:20
That is lambda square plus 7 lambda plus 6 is equal to 0.
01:26
Splitting the middle term, we get lambda square plus 6 lambda plus lambda plus 0.
01:35
Factor out lambda from first two terms and plus 1 from last 2 terms.
01:40
We get lambda times lambda plus 1, plus 1 times lambda plus 4.
01:46
This is 6.
01:47
6 is equal to 0.
01:50
Now factor out lambda plus 6, we are left with lambda plus 1 is equal to 0.
01:58
Equating both the sectors with 0, we get lambda is equal to negative of 6 and lambda is equal to negative of 1.
02:06
These are the two eigen values of the given matrix a.
02:11
Now for the second subpart, we need to obtain the values of eigen vectors for the given matrix a.
02:23
For that, we will obtain the value of a minus lambda i times x and integrate it with 0.
02:37
Now, the values of lambda are negative of 1 and negative of 6...