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Using Dimension Formula of a Matrix

  1. Oct 15, 2011 #1
    1. The problem statement, all variables and given/known data
    If VΩW contains only the zero vector, then dim(V+W)+dim(VΩW) = dim(v) + dim(W) becomes dim(V+W) = dim(v) + dim(W). Check this when V is the row space of A, W is the nullspace of A, and the matrix A is mxn of rank r. What are the dimensions?


    2. Relevant equations

    dim(V+W)+dim(VΩW) = dim(v) + dim(W)

    3. The attempt at a solution

    I don't even know how to start this problem.

    I do know that dim(V+W) + dim (VΩW) = rank of [A B] + nullity of [A B]

    Can anyone help??? Thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 16, 2011 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    It would help if you told us what thes symbols mean. I presume that V and W are vectors but what is [itex]\Omega[/itex] and what do you mean by [itex]V\Omega W[/itex]?
     
  4. Oct 16, 2011 #3
    I'm sorry! That symbol means V intersects W... And yes, V and W are vectors.
     
  5. Oct 16, 2011 #4

    Mark44

    Staff: Mentor

    No, V and W are vector spaces.
     
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