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Linear Algebra - Find an equatio relating a,b,c

  1. Jun 27, 2010 #1
    1. The problem statement, all variables and given/known data

    http://i.imgur.com/FuMGN [Broken]

    2. Relevant equations

    3. The attempt at a solution

    I know that for a linear system to be consistent it must have one or more answers.

    After some row operations I get this matrix: http://i.imgur.com/KTEkF [Broken]

    I know that if I have a row of zeros that I have a trivial solution, so do I need to equate b-a-c to zero?

    B - A - C = 0?
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jun 27, 2010 #2


    Staff: Mentor

    Think about what the augmented matrix represents: Ax = c, where A is your 3 x 3 matrix, x is the vector <x, y, z>, and c is the vector of constants, <a, b, c>.

    The bottom row means 0x + 0y + 0z = b - a - c. Regardless of the values of x, y, and z, what is the only value that the right side could have to make an equation that had a solution?
  4. Jun 27, 2010 #3
    Zero. So the relationship between a,b, and c is b-c-a=0, correct?
  5. Jun 27, 2010 #4


    Staff: Mentor

    Right. So the system of equations is consistent provided that b - c - a = 0. If two variables are specified, the third can be found. That means that there are two free variables, and therefore, the set of points in R3 for which the system of equations is consistent is a plane in space.
  6. Jun 27, 2010 #5
    Thank you for the help.
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