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Subspace problems

  1. Aug 23, 2007 #1
    1. The problem statement, all variables and given/known data

    Which of the following subsets of R^n*n are in fact subspaces of R^n*n

    1) The symmetric matrices
    2) The diagonal matrices
    3) The nonsingular matrices
    4) The singular matrices
    5) The triangular matrices
    6) The upper triangular matrices
    7) All matrices that commute with a given matrix A
    8) All matices such that A^2 = A
    9) All matrices such that trace(A) = 0

    Can anyone give me a detailed solution for this questions?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 23, 2007 #2
    First of all, what are the qualities a subset needs to have to be a subspace of R^n*n?
     
  4. Aug 23, 2007 #3

    Dick

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    Homework Helper

    No one will 'give you a detailed solution', they will only help you to arrive at your own solution. nicktacik has suggested how to start thinking about the problem. I suggest you start.
     
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