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Math Help - Eigenvector (if v1 and v2 are equal)

  1. #1
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    Eigenvector (if v1 and v2 are equal)

    One eigenvalue is 2.
    A= |-1 3| |2 0|

    -3x+3y=0
    2x-2y=0

    x=y

    I don't know the answer
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  2. #2
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    Hi
    Could you explain better what you are looking for ?
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  3. #3
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    Quote Originally Posted by running-gag View Post
    Hi
    Could you explain better what you are looking for ?
    I should find eigenvectors of A matrix.

    A= |-1 3| |2 0|
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  4. #4
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    OK so your beginning is correct
    With eigenvalue = 2, you find x=y
    Therefore (1,1) is an eigenvector
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  5. #5
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    Quote Originally Posted by JrShohin View Post
    One eigenvalue is 2.
    A= |-1 3| |2 0|

    -3x+3y=0
    2x-2y=0

    x=y

    I don't know the answer
    Suppose you have an eigenvector X for an eigenvalue k
    Then A.X = kX
    And for every p real
    A.(pX) = p A.X = p kX = k (pX)
    Therefore pX is also en eigenvector

    This is why when you try to solve your system you find 2 equivalent equations
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  6. #6
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    In fact, the set of all vectors v such that Ax= \lambda x, for \lambda and eigenvalue of a A is a subspace. That's why you cannot solve for just a single pair of values for x and y. You arrived at y= x so <x, y>= <x, x>= x<1, 1> or all mutiples of <1, 1> are eigenvectors corresponding to eigenvalue 2. That is the "eigenspace" for eigenvalue 2.
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