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Diagonalization of Linear Operator

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Consider the linear operator T:R^3 given by T (see attached)

Determine the eigenvectors and the corresponding eigenvalues of T. If T diagonalizable? Why or why not?

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Solution Summary

Checking if the given linear operator is diagonalizable by calculating its eigenvalues and eigenvectors. Attached as a Word file.

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Solution:
Since , the matrix of this linear operator is .
The eigenvalues we find from the equation :

There are two different eigenvalues: and .
Let's find the corresponding eigenvectors.
For the eigenvector have to be solution of the homogeneous system of equations with matrix ...

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