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# find eigenvalues

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Given the following matrices A, B, and C compute the eigenvalue and eigenvector for each matrix.
A =(-2, 6, 6, 3)
B= (4, 2, -1, 6)
C= (0, -1, 1, 2)

##### Solution Summary

This solution carefully finds eigenvalues. Matrices are computed for A, B and C.

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To find eigenvalues:
Calculate the characteristic polynomial
(1.1)
Find the roots of the equation
(1.2)
These are the eigenvalues
To find the eigenvectors, for each eigenvalue solve the system of equations
(1.3)
Note that for any constant and eigenvector v, the vector is an eigenvector as well with the same eigenvalue:

Case 1:

Then:

(1.4)
Equating it to zero we find two roots:

(1.5)
To find the eigenvectors we ...

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