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    Matrices

    Which of the matrices below are diagonalizable and which are not?Explain your answer.

    i)


    ii)

    HINT: In both cases the only eigenvalues are λ=-1 and λ=2.
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    Hello,

    Quote Originally Posted by matty888 View Post
    Which of the matrices below are diagonalizable and which are not?Explain your answer.

    i)


    ii)

    HINT: In both cases the only eigenvalues are λ=-1 and λ=2.
    Find the eigenspaces associated to each eigenvalue.
    If the sum of their dimension is 3, then it's diagonalisable.
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    Quote Originally Posted by matty888 View Post
    Which of the matrices below are diagonalizable and which are not?Explain your answer.

    i)


    ii)

    HINT: In both cases the only eigenvalues are λ=-1 and λ=2.
    An n x n matrix A is diagonalizable if and only if it has n linearly independent eigenvectors .....
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