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Vector equations

  1. Apr 10, 2007 #1


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    Gold Member

    1. The problem statement, all variables and given/known data
    A is a mxn matrix and B is a nxm matrix. AB = Im.
    a) Prove that there's only one solution to Bx = 0 where x and 0 are coloum vectors.
    b) Prove that m<=n

    2. Relevant equations
    if A is a mxn n>m then there're infinite solutions to Ax=0

    3. The attempt at a solution
    a) Bx=0 => ABx=A0 => Ix=0 => x=0 so there's only the trivial solution.
    b) according to the equation above if m>n then there would be an infinite amount of solutions to Bx=0 and not only one.
    Did I do that right? This was a problem on an exam and it relative to the other questions it looks to easy.
  2. jcsd
  3. Apr 10, 2007 #2


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    Homework Helper

    Hm, looks okay.
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