1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Mark44

    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

    Mark44

    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solving a Matrix with variables
  1. Solving For A Variable (Replies: 5)

  2. Solving for a variable (Replies: 1)

  3. Solve Unknown Variable (Replies: 5)

Loading...