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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 Preview

    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 ...

    Solution Summary

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