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Find matrixes B and C?

  1. Mar 11, 2012 #1
    1. The problem statement, all variables and given/known data


    A matrix B is symmetric if B=transpose B.

    A matrix C is skew-symmetric if C=−transpose C.

    Let A be the matrix given by

    A=[[3,6],[-2,1]]

    Determine any symmetric matrix B and any skew-symmetric C such that A=B+C

    2. Relevant equations

    All given above. Don't know if I need any more.

    3. My attempt and issue

    I think two equations can be made A =B+C and A = BT - CT
    Don't know how to solve them
     
  2. jcsd
  3. Mar 11, 2012 #2
    It's been awhile since I've done matrices, but I'll give it a shot. I believe your two equations are correct, you just need to solve for B and C.

    Here is what I would do: Solve for either B or C in the first equation ( [itex]A = B + C[/itex] ), plug it into the second equation and use this property: [itex](A+B)^{T}=A^{T}+B^{T}[/itex]. See if that gets you anywhere!
     
  4. Mar 11, 2012 #3

    Dick

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    A+A^T is symmetric, and A-A^T is antisymmetic, yes? Tell me why? Can you think of some way to combine them to get A?
     
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