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Homework Help: Gaussian Elimination matrix

  1. Jan 3, 2012 #1
    1. The problem statement, all variables and given/known data
    What is the Gaussian elimination matrix for the vector for the vector [itex]v=(2,-10,16,2)[/itex]?


    3. The attempt at a solution
    I don't understand the question. What is a "Gaussian elimination matrix for a vector?" I know that Gaussian elimination is a method for solving a system of linear equations, but I'm not sure what is meant/how to find the Gaussian elimination matrix, given a vector. Can someone please explain this to me?

    Thanks
     
  2. jcsd
  3. Jan 4, 2012 #2

    Mark44

    Staff: Mentor

    I'll take a stab at it, since no one else has replied.

    [tex]\begin{bmatrix} 1 & 0 & 0 & 0 & | & 2 \\
    0 & 1 & 0 & 0 & | & -10 \\
    0 & 0 & 1 & 0 & | & 16 \\
    0 & 0 & 0 & 1 & | & 2 \end{bmatrix}[/tex]

    What I'm showing here is a row-reduced augmented matrix that represents a system, for which the solution is the vector <2, -10, 16, 2>.
     
  4. Jan 5, 2012 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    My guess would be that if you regard v as a _column_ vector they want you to determine the matrix E such that Ev becomes a simple unit vector, such as (1,0,0,0)^T,or maybe (2,0,0,0)^T. After all, that is how Gaussian elimination works: we determine linear combinations of rows such that a column is simplified; row operations = multiplication on the left by a matrix. (Or, maybe they want v to be a row vector, just as written, in which case they want a matrix E such that vE = something simple, like (2,0,0,0).)

    RGV
     
  5. Jan 5, 2012 #4
    Thanks for the replies guys but I've solved this problem. In case you were wondering, I needed to find a matrix such that the image of the vector (2,-10,16,2) is the vector (2,-10,16,0). Pretty simple, I was just confused as to what exactly a "gaussian elimination matrix" was. :smile:
     
  6. Jan 5, 2012 #5

    Mark44

    Staff: Mentor

    This is this question you should have asked.
     
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