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Linear Algebra (Symmetric Matrix)

  1. Dec 14, 2012 #1
    A 3x3 symmetric matrix has a null space of dimension one containing the vector (1,1,1). Find the bases and dimensions of the column space, row space, and left null space.

    I understand how to get the Dim of Col(A), Row(A), and Nul(A^T) but how do i get the bases with just knowing the dimension of one vector? How should I approach this?
  2. jcsd
  3. Dec 14, 2012 #2


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    Hey MoBaT.

    Can you pick any linearly independent basis?
  4. Dec 14, 2012 #3
    Dosen't say anything against it. I know what the answer is becuase he gave it to us. It was like:

    Dim of Col(A) = 2, dim Row(A) = 2, Dim Nul(A^T) = 1
    Basis Row(A) = {[-1 1 0], [-1 - 1]}. Because A is symmetric, Col(A) = Row(A) and Nul(A^T) = Nul(A).

    I understand everything after the Basis row(A) but do not understand how he got that Row(A)
  5. Dec 14, 2012 #4
    Found out how to do it. Pretty much fill in the rest of the information with the identity matrix.
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