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Homework Help: Solving a Matrix with variables

  1. Jan 16, 2013 #1
    1. The problem statement, all variables and given/known data

    Find all values of k, if any, that satisfy the equation.

    [2 2 k]*[1 3 0; 3 0 5; 0 5 -1][2 ; 2 ; k]=0

    2. Relevant equations

    3. The attempt at a solution

    Multiplying the two matrices on the right

    [2 2 k] * [8 ; 6 +5k ; 10-k]=0

    Multiply again

    [ 16 + 10+12k + 10k-k^2]=0

    I'm stuck here, because I'm really confused about whether this is a homogeneous matrix or not, or if there are infinite solutions to k because the variable just needs to be zero.

    Thanks for any help :)
  2. jcsd
  3. Jan 16, 2013 #2


    Staff: Mentor

    I'm not sure I understand your notation, but it looks for the matrix product to be zero, you need 16 + 10+12k + 10k-k^2 = 0. That's a quadratic equation, so should be easy to solve for k.
  4. Jan 16, 2013 #3
    I've left it in matlab notation, so the semi colons indicate a new row and spaces mean the next entry is in the next column.

    Thanks for helping me clear that up, I used the quadratic equation to solve for k but I got the roots 10±8[itex]\sqrt{2}[/itex] which are apparently incorrect. Perhaps it's at this point an error with my online homework system. Oh well.
  5. Jan 17, 2013 #4


    Staff: Mentor

    You transposed a couple of numbers. It should be 16 + 12 + 10k + 10k - k^2 = 0
    This part is irrelevant - the exercise is to find values of k for which the matrix product is 0.
  6. Jan 17, 2013 #5
    I believe I made a typo here in entering, as I still return [itex]10\pm8\sqrt{2}[/itex] as the roots. The problem has been solved though, my instructor sent an email regarding the error with the homework system.

    Again, thank you for your help!
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