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Choice of variable to make matrix rank = 1

  1. Mar 19, 2010 #1
    1. The problem statement, all variables and given/known data
    What choice of d would make matrix
    a b
    c d
    have a rank of 1?

    2. Relevant equations
    rank(A) + nullity(A) = n
    3. The attempt at a solution
    In order for rank = 1, then nullity must = 1 because n = 2.
    This isn't a nonsingular matrix, so det(A) = ad-bc =/= 0.
    d = bc/a, where 'a' cannot be 0.
    Let's say a = 1, then the matrix will be
    1 ad/c
    c d
    c cannot be 0 either, so matrix is now
    1 d
    1 d
    and I guess a possible candidate would just then be
    1 1
    1 1?

    I think I'm supposed to give the answer in more arbitrary terms, so I am lost here.
     
  2. jcsd
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