1. Limited time only! Sign up for a free 30min personal 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!

Which are the pivot columns? - Linear Algebra

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data
    Given matrix

    A=

    1 1 -2 1 3
    2 -1 2 2 6
    3 2 -4 -3 -9

    x=

    x1
    x2
    x3
    x4
    x5

    b =

    1
    2
    3

    1. Solve the system by elimination (use the augmented matrix) until pivots are found (no backward elimination here).

    2. Show that pivots are respectively 1 and -3, and indicate clearly which are the pivot columns and free columns.


    2. Relevant equations

    Matrix A and vector b



    3. The attempt at a solution

    I perform elimination on augmented matrix to solve part 1.

    1 1 -2 1 3 | 1
    0 -3 6 0 0 | 0
    0 -1 2 -6 -18 | 0


    1 1 -2 1 3 | 1
    0 -3 6 0 0 | 0
    0 0 0 -6 -18 | 0

    What I don't understand is part 2.

    As far as I know, for an entry to become a pivot it must be the first non-zero entry on the row and there must be no non-zero entries under it.

    1 1 -2 1 3 | 1
    0 -3 6 0 0 | 0
    0 0 0 -6 -18 | 0

    If that rule applies I would find three pivots instead of two. (1,-3, -6) I know the right answer for this exercise is that there are only two pivots (1, -3), resulting col1 & col2 to be the pivot columns and the rest are free columns.

    Can someone explain why -6 is not a pivot in this case?
     
  2. jcsd
  3. Oct 18, 2011 #2

    Mark44

    Staff: Mentor

    I don't see an error on your part. Are you sure you have copied the matrix correctly?
     
  4. Oct 18, 2011 #3
    as far as I could tell, there should be 3 pivots in your reduced matrix.

    I suspect that you wrote the matrix down wrong, because if you make the last row
    -3 3 -4 -3 -9 instead of 3 3 -4 -3 -9, then there should be only two pivots.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Which are the pivot columns? - Linear Algebra
  1. Find pivot columns (Replies: 1)

Loading...