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!

Are the columns linear independent?

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

    Were the columns of A linearly independent?
    The matrix A is given in row reduced echeleon form
    1 2 0 0
    0 0 1 0
    0 0 0 1


    2. Relevant equations
    Hint: Consider the solution set to A x = 0


    3. The attempt at a solution
    I think that the colums were linearly dependent since the first two columns in their row reduced forms are multiple of each other. Is that correct? If yes, and my explanation seems logical, then why is the hint given?
     
  2. jcsd
  3. Mar 2, 2010 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Perhaps they want you to see why "the first two columns in their row reduced forms are multiple of each other" implies that the columns of A are linearly dependent. In other words, the definition of linear independence says the vectors v1, v2, v3, and v4 are independent if the only solution of c1 v1+c2 v2+c3 v3+c4 v4=0 is c1=c2=c3=c4=0. How does what you said about the row-reduced matrix lead to the conclusion that the original columns of A are linearly dependent according to the definition above?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Are the columns linear independent?
  1. Linear Independence (Replies: 9)

  2. Linear independence (Replies: 3)

  3. Linear independence (Replies: 3)

  4. Linear Independence (Replies: 2)

Loading...