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Eigenvalues and eigenvectors

  1. Apr 7, 2010 #1
    Hey guys,

    I'm studing to my exams now, and I came accors this question i eigenvectors where you find them and bla bla. There is part to it which asks to express vetor

    X= [2/1]

    as a linear combination of eigenvectors. Hence calculate B2X, B3X, B4X and B51X, simplifying your answers as much as possible.

    How do you do the linear combination?

    Thanks!
     
  2. jcsd
  3. Apr 7, 2010 #2

    HallsofIvy

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    Staff Emeritus
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    The "bla bla" does not help at all. Perhaps you could post the entire question?

    For example, what does "[2/1]" mean? Is that a two dimensional vector with components 2 and 1? Write it as a linear combination of what eigenvectors? Is there some matrix or linear transformation you haven't mentioned? And what are " B2X, B3X, B4X and B51X"? Those are not standardized notations.
     
  4. Apr 7, 2010 #3
    Ok sorry I suppose I didn't make myself clear.

    I have two eigenvectors.

    First: Look at 1.jpg
    Second : Look at 2.jpg

    The vector X (look at 3.jpg) is to be written as a linear combination of eigenvectors. How do you do that? It's just a theory I'm interested in not solution to the question.

    Thanks and sorry for inconvenience.
     

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  5. Apr 8, 2010 #4
    OK, now your question is clear. Let v1=(-3,1) be the first eigenvector, and v2=(-2,1) the second one. Now you want "a1" and "a2" such that

    X = a1 v1 + a2 b2

    That is equivalent to solving a linear system

    [2] = [-3 -2] [a1]
    [1] [ 1 1] [a2]

    Where the eigenvectors went as columns.
     
  6. Apr 8, 2010 #5
    So the answer should look like this (look at the ans.jpg)?
    And are a1 and a2 variables?

    Thanks a lot!
     

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  7. Apr 8, 2010 #6
    correct! :)
     
  8. Apr 8, 2010 #7
    Thanks a lot jrlaguna!
     
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