1. Not finding help here? Sign up for a free 30min 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!

Find value h so the matrix has infinitely many solutions?

  1. Sep 16, 2005 #1
    Hello everyone i'm confused on what i'm suppose to do to solve this matrices.
    |7 -7|5 |
    |21 h|15|

    What am I trying to make h be? I row reduced to get
    |7 -7 |5|
    |0 21+h |0|
    So if i let h = -21 will this make it have infin. solutions? because then i would have 0 0 0?
     
  2. jcsd
  3. Sep 16, 2005 #2

    TD

    User Avatar
    Homework Helper

    Indeed, by doing so you create 2 lineair dependant equations so when reduving, one cancels out as a 0 row. You then have 1 equation in 2 unknowns, giving an infinite set of solutions.
     
  4. Sep 16, 2005 #3
    Thanks! this brings up another question..
    I'm supppose to find a value of k that will make it have no solutions.
    I have:
    |1 1 4 2|
    |1 2 -4 3|
    |6 13 k 20|

    -6R2 + R3 -> R3
    |1 1 4 2|
    |1 2 -4 3|
    |0 1 24+k 2|

    now if i let k = -24 will this make it have no solutions? because 0 cannot equal 2 right?
     
  5. Sep 16, 2005 #4

    TD

    User Avatar
    Homework Helper

    Then it would say in the last row: 0 1 0 2, which is still possible since then you have y = 2. You have to reduce it further to see it, I think :smile:
    You could also compute the determinant of the coëfficiënt matrix and let it equal 0, solve for k.
     
  6. Sep 16, 2005 #5
    When i keep trying to reduce it gets bad...
    I ended up with
    |1 1 4 2|
    |2 3 0 5|
    |0 0 -20-k 0|
    and now i'm stuck, anyu ideas?
     
  7. Sep 16, 2005 #6

    TD

    User Avatar
    Homework Helper

    That's strange, perhaps you made some mistakes because that doesn't seem right to me.
    Check your work again or use the other method I gave.
     
  8. Sep 16, 2005 #7
    reduce the matrix in row echelon form,and follow the rules to solve it..its simple
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?