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!

Proving a Linear System

  1. Apr 14, 2010 #1
    1. The problem statement, all variables and given/known data

    Show that rank(A+B) [tex]\leq[/tex] rank(A) + rank (B)

    for every A,B [tex]\in[/tex] Mm,n (Real)

    2. Relevant equations

    N/A

    3. The attempt at a solution

    i only know how to proof this

    rank(AB) [tex]\leq[/tex] rank(A) or rank(B),



    and can this "rank(AB) [tex]\leq[/tex] rank(A) or rank(B)" help me to prove the above statement? can someone help me, to prove the above statement
     
  2. jcsd
  3. Apr 14, 2010 #2
    I'm not really sure whether it's a fine proof, so please correct me. And forgive my English, never read anything abt algebra in English :).

    Let A and B be nxm matrices. Let's consider their columns as the columns of vector coordinates over the same vector space. Now rank(A) and rank(B) are the numbers of lineary independent vectors in each matrix respectively. Adding those two matrices, you are adding vectors. As there can be some linear dependencies between vectors in A and B, rk(A+B) can not overcome rk(A)+rk(B), as it still is nxm matrix. Basically speaking, by taking linear combinations of vectors, you can not get an independent vector, according to the very deffinition itself.

    Huh, I hope one can understand what I wanted to write ;).
     
  4. Apr 14, 2010 #3
    thanks i get it, and i will try convert that to mathematical form,

    thank you
     
  5. Apr 14, 2010 #4

    lanedance

    User Avatar
    Homework Helper

    yep, good thinking
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proving a Linear System
  1. Proving a Linear System (Replies: 12)

  2. Proving a Linear System (Replies: 19)

Loading...