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Show that H is a subspace of M sub2x2, by finding a subset of H such that span(S) = H

  1. Apr 2, 2010 #1
    H = ([a,b;c,d] : a+d =0}

    Dim(M2x2)= 4, so a basis would have 4 components?

    I got this far and am stuck.

    [a, b ; c , -a] = a[1,0; 0,-1] + b[0, 1;0,0] +c[0,0; 1,0]
     
  2. jcsd
  3. Apr 2, 2010 #2

    Mark44

    Staff: Mentor

    Re: Show that H is a subspace of M sub2x2, by finding a subset of H such that span(S)

    A basis for M2x2 would have 4 vectors/matrices, but how many would be in a basis for H?
    Now, do these matrices span H? I.e., can every matrix in H be written as a linear combination of the three matrices above?

    What's left to do is to show that H is a subspace of M2x2. To do this, you need to show three things:
    That the zero matrix is in H.
    That if A and B are in H, then A + B is in H.
    That if A is in H and c is a scalar, then cA is in H.
     
  4. Apr 2, 2010 #3
    Re: Show that H is a subspace of M sub2x2, by finding a subset of H such that span(S)

    Thank you
     
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