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About basic eigenvector questions

  1. Oct 12, 2014 #1
    1. The problem statement, all variables and given/known data

    1. If v is any nonzero vector in R^2, what is the dimension of the space V of all 2x2 matrices for which v is an eigenvector?

    2. If v is an eigenvector of matrix A with associated eigenvalue 3, show that v is in the image of matrix A

    2. Relevant equations

    If v is an eigenvector with eigenvalue c(real number), then Av=cv (definition of eigenvector)

    3. The attempt at a solution

    i have posted a picture for my attempt at the first question
    but i totally have no idea on the second question
    need help from you guys!
    Last edited: Oct 12, 2014
  2. jcsd
  3. Oct 12, 2014 #2

    Attached Files:

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