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Homework Help: Finding the value of a variable in a matrix

  1. Oct 20, 2014 #1
    1. The problem statement, all variables and given/known data
    Given :

     x+y+5z = 2

     x+2y+7z = 1

     2x−y+4z = a
    a) Determine the value of a which will make the given system have many solutions. Explain your answer.
    b) Choose a value of a which will make the given system have NO solutions. Explain your answer.
    c) Is it possible to choose a value of a, which will make the given system have exactly one solutions? Explain
    your answer.

    2. Relevant equations

    3. The attempt at a solution
    I found the reduced matrix of the system of equations and got,
    1 0 3
    0 1 2
    0 0 0
    , but am not sure on what to do next.
  2. jcsd
  3. Oct 21, 2014 #2


    Staff: Mentor

    You need to set up an augmented matrix whose fourth column contains the constants on the right sides of your equations.
  4. Oct 21, 2014 #3


    User Avatar
    Science Advisor

    Equivalently, don't use matrices at all!
    You have:
    x+y+5z = 2
     x+2y+7z = 1
     2x−y+4z = a

    Subtract the first equation from the second to get y+ 2z= -1.
    Subtract the third equation from twice the first equation to get 3y+ 6z= 4- a

    Subtract three times the first of those equations from the second to get 0= 7- a.

    For what value of a is that true? So for what value of a does the original set of equations have an infinite number or solutions? For what values of a does it have no solution?
  5. Oct 21, 2014 #4
    thank you I understand how to do it now!
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