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!

Question about row/column/nullspace

  1. Apr 12, 2017 #1
    1. The problem statement, all variables and given/known data
    If we have a 3x5 matrix:

    The row space is in r5, the col space is in r3, and the nullspace is in r3 correct?
    Because you would need 5 components to be a member of r5 so the col space cannot be a member of r5 correct?

    Here is the question: http://prntscr.com/evo91g



    2. Relevant equations


    3. The attempt at a solution
    Am I getting something fundamentally wrong here? Or is the question just wrong? I believe I'm right for reasons mentioned above.
     
  2. jcsd
  3. Apr 12, 2017 #2

    Math_QED

    User Avatar
    Homework Helper

    The nullspace is a subspace of ##\mathbb{R}^5##, right? Therefore the nullspace is not in ##\mathbb{R}^3##. For the rest you seem correct. It seems the question is wrong.
     
  4. Apr 12, 2017 #3
    Why would it be in r5 though? Each vector in the nullspace will only have 3 components
     
  5. Apr 12, 2017 #4

    Math_QED

    User Avatar
    Homework Helper

    Can you give me your definition of null space?
     
  6. Apr 12, 2017 #5
    The subspace of linear combinations that make your system equal to 0?

    edit: Now that I think about it, when A is a 3x5 matrix, you need a 5x1 matrix vector X. Since X is 5x1, that means the nullspace is in r5 since X represents all vectors inside the nullspace?
     
  7. Apr 12, 2017 #6
    The null space and the row space of a matrix will always be sub-spaces of the same vector space (why?).The column space and row space of a matrix will be sub-spaces of the vector space whose dimension is the number of elements in the vector. So if we have a 12x23 matrix, its row space is a sub-space of R23 and its column space is a sub-space of R12. From here I assume you can figure out the correct solution.
     
  8. Apr 12, 2017 #7
    Yup! Makes sense now. Just find it interesting that I understand the nullspace and can compute it easily but I still abstract details like that.
     
  9. Apr 13, 2017 #8

    Math_QED

    User Avatar
    Homework Helper

    Yes, your reasoning is correct. That's a very bad definition of null space, though.

    A better definition would be: Let ##A## be an ##m \times n## matrix.

    ##Null(A) := \{x \in \mathbb{R}^n| Ax = 0\}##

    Or if you are familiar with linear mappings: Let ##f: V \rightarrow W## be a linear mapping:

    ##Ker(f) := \{x \in V|f(x) = 0\}##
     
    Last edited: Apr 13, 2017
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: Question about row/column/nullspace
  1. Nullspace Question (Replies: 1)

Loading...