Question #26f69
2 Answers
The eigenvalues are
Explanation:
The matrix is
To calculate the Eigenvalues, calculate the determinant
where
The determinant is
The caracteristic polynomial equation is
The solutions are
Explanation:
We are looking for:
Where A is a
K is proportional to X, i.e.
So we are really looking for:
Rearranging:
Factor:
Where I is the identity matrix, and therefore:
We know that this can only have a non zero solution, if the determinant of
The above relies on you knowing the theory of linear dependence and independence, and it's role in solving homogeneous systems. I am assuming you would know this before dealing with eigenvalues.
Since we require a non zero solution we need to solve:
So we find the determinant:
By quadratic formula:
So these are the eigenvalues of A.
For further help, watch MIT's OpenCourseWare video.
Introduction to Linear Algebra with Gilbert Strang.
Gilbert Strang is an amazing teacher and makes it so much easier to understand.
This is the link for the video on eigenvalues and eigenvectors.
Hope it helps.