Results 1 to 2 of 2

Math Help - subspaces of Rn

  1. #1
    Member
    Joined
    Oct 2010
    Posts
    127

    subspaces of Rn

    Determine whether the following three sets are a subspace of Rn. If it is, show that the the 3 subspace properties are satisfied, and if it is not, show by example that one of the properties fails.

    1. The set of solutions of Ax= x, where A is any n x n matrix.

    2. The first quadrant in R2. That is: {[x_1, x_2] ∈ R2| x_1 ≥ 0 and x_2 ≥ 0}

    3. {[x_1, x_2] ∈ R2| (x_1 ≥ 0 and x_2 ≥ 0) or (x_1 0 ≤ and x_2 ≤ 0)}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2010
    From
    Staten Island, NY
    Posts
    451
    Thanks
    2
    You should show the work that you've attempted so we know where you're stuck. I'll do the first one:

    A\cdot 0=0

    If Ax=x and Ay=y, then A(x+y)=Ax+Ay=x+y

    If Ax=x and c is a scalar, then A(cx)=cAx=cx

    So it is a subspace.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. subspaces...
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 28th 2011, 01:20 PM
  2. Replies: 0
    Last Post: October 13th 2009, 04:48 PM
  3. Subspaces
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 8th 2009, 10:18 AM
  4. Subspaces
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 26th 2009, 07:55 PM
  5. Subspaces
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: March 14th 2009, 06:50 PM

Search Tags


/mathhelpforum @mathhelpforum