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!

Concept of Invertible Matrices

  1. Oct 30, 2008 #1
    1. The problem statement, all variables and given/known data

    If A is an invertible square matrix, then Ax = b is consistent for each b in R^n

    2. The attempt at a solution

    If A multiplied by A inverse is identity, then it would always be consistent. So I thought , if A is just randomly multiplied by some x, then it will still be consistent right? I can't seem to find anything wrong with the statement above.
     
  2. jcsd
  3. Oct 30, 2008 #2
    I think Ax = b holds true regardless of A being invertible or not
     
  4. Oct 30, 2008 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Ax=b is not exactly 'true' if there no solutions x to the equation given a b. If A is invertible then A^(-1)Ax=Ix=x=A^(-1)b. So given any b, x=A^(-1)b. Yes, it's consistent.
     
  5. Oct 31, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I have no idea what you mean by this. What is "Ax= b" that it could "hold true"? Certainly if A is a matrix and x a vector with as many components as A has columns, then there exist a vector b such that Ax= b. Is that what you meant?

    If A is invertible, then given any such vector b, there exist a vector x such that Ax= b.

    If A is not invertible then, given b, there may not exist such an x or there may exist an infinite number of the them.
     
  6. Oct 31, 2008 #5
    Thanks for the help guys. That little algebra helped me see it properly Dick.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Concept of Invertible Matrices
  1. Invertible matrices (Replies: 5)

  2. Invertible functions (Replies: 8)

Loading...