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Linear Algebra partitioned matrix and vector theoretical question

  1. Oct 29, 2011 #1
    1. The problem statement, all variables and given/known data

    Let X be an invertible 2011 X 2011 matrix, let I be the 2011 identity matrix.

    Let B=[[X,I],[I,X-1]] and let p=e1+e2+e3+....+e2011.

    (The terms in the square brackets represent the rows of the matrix, so [X,I] is the first row)

    Find a non-zero vector q, such that Bq=0.

    Use partitioned matrix notation to write q explicitly in terms of p , and to display the calculation which shows that Bq=0.


    3. The attempt at a solution

    None. I have no idea what to do. The only thing that stands out to me is that
    q is a 4022 X 1 vector and that p is a 2011 X 1 vector, so q must look something like:

    q=([tp],[sp]) where t and s are real numbers
     
  2. jcsd
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