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!

Invertible 3x3 matrices a subspace of 3x3 matrices

  1. Jul 11, 2010 #1
    1. The problem statement, all variables and given/known data

    Is the set of invertible 3x3 matrices a subspace of 3x3 matrices?

    2. Relevant equations



    3. The attempt at a solution
    I think no - the 'neutral 0 element' is not in the subset since the 3x3 0 matrix is not in the subset. Am I right? The book says it's not a subspace because it's not closed under addition, but I'm not sure if my reason is also correct.
     
  2. jcsd
  3. Jul 11, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Your reason is also correct.
     
  4. Jul 11, 2010 #3
    thanks! also, quick question: does the 'neutral 0 element' mean the additive identity?
     
  5. Jul 11, 2010 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Sure, subspace generally means closed under linear combinations. The zero matrix is the identity.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Invertible 3x3 matrices a subspace of 3x3 matrices
  1. Invertible matrices (Replies: 3)

Loading...