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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

    A.

    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)=1

    ??

    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

    rho(A)=0



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



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

    lanedance

    User Avatar
    Homework Helper

    this is pretty hard to follow prove what?
     
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