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!

Reverse-engineering a system of linear equations from solution, using matrices

  1. Jan 14, 2010 #1
    1. The problem statement, all variables and given/known data

    Find a system of linear equations, with 3 unknowns, given that the solutions are the points (1,1,1) and (3,5,0) on a line.

    2. Relevant equations

    None

    3. The attempt at a solution

    A solution that lies on a line tells me that I'm looking at the line of intersection between 2 planes. I'm supposed to be using matrices to solve this, but I've only ever done so in the other direction: taking a system of linear equations and reducing them to reduced-row-echelon-form to find the solution set.

    Since there are infinitely many solutions, there must be at least 1 dependent variable. I figured that I would need to first find the equation for the line from the points of the solution, but I ended up with this:

    (x-1)/2 = (y-1)/4 = (z-1)/-1

    which only confused me more. Then I tried to formulate an augmented matrix to try and find the coefficients of the linear equations, but didn't get very far after reduction, and I realized that I was still missing the right hand side of the matrix:

    [a 0b 2.5c ?]
    [0a b -1.5c ?]

    And this is where I stand. Any help is much appreciated.
     
  2. jcsd
  3. Jan 15, 2010 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Showing that this line is the intersection of the planes given by (x-1)/2= (y-1)/4 and (x-1)/2= (z-1)/(-1) which are the same as 4(x-1)= 2(y-1) or 4x- 2y= 2 and -(x-1)= 2(z-1) or x+ 2z= 3. That is, those points satisfy 4x- 2y= 2 and x+ 2z= 3. That's your system of equations.

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

Have something to add?
Similar Discussions: Reverse-engineering a system of linear equations from solution, using matrices
Loading...