Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Independant proof 2009c86 1A,B

  1. Jun 22, 2011 #1
    this is a two part question:

    v1..vn is a basis

    of R^n

    and there is a vector b which belongs to R^n and b differs the sero vector


    proof that {v1-vn,v2-vn,...,vn-1 - vn}

    by definition

    in order to prove that a group is independant

    we need to show the the only way for

    a1(v1-vn)+a2(v2-vn) ..+an(vn-1 -vn)=0

    is a1=..=an=0 all the coefficient hs to be zero

    so it rang a bell "i need to get a trivial solution "

    but trivilal solution is in Ax=0 system could be should if |A| differs zero.

    but A is a square matrices by difinition.

    how to construct from this single equation a square matrices?


    the second question:

    if v1..vn are solutions to Ax=b system then



    rho(A) is the dimention of row or column space

    if v1..vn are solving this system

    then the dimention of the solution space is n dim(P(A))=n

    and from the formula where n=dim(P(A))+rho(A) we get n=n+rho(A)

    so i got


    but i am asked to prove that rho(A)=1

    where is my mistake
  2. jcsd
  3. Jun 22, 2011 #2


    User Avatar
    Homework Helper

    this is pretty hard to follow prove what?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook