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!

Finding a basis for the range space

  1. Mar 7, 2016 #1
    1. The problem statement, all variables and given/known data
    image.jpg

    I've found the dimension of V to be 3.
    According to the solutions, it seems that the basis can be written straight away, { (1,1,1,2), (1,2,-3,1), (3,4,-1,5) } (which is also the basis for the column space of the matrix), without verifying the vectors are linearly independent.. how come? The vectors in the matrix are not necessary linearly independent..
     
  2. jcsd
  3. Mar 7, 2016 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Those three vectors cannot be a basis of anything, because they are linearly dependent. You can choose any three other columns to get an independent set.
     
  4. Mar 7, 2016 #3
    Oh right.. I know how to do already, thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding a basis for the range space
  1. Basis of matrix space (Replies: 4)

  2. Find range (Replies: 2)

Loading...