1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear algebra

  1. Jan 26, 2009 #1
    in this question i am given 2 subspaces of R4

    W={(x1,x2,x3,x4)[tex]\in[/tex]R4|x1-x4=0}

    U=sp{(1,2,0,-1),(2,3,1,-1),(1,-1,1,-1)}

    and am asked to find
    1] a basis and dimention for W
    2] a basis for W+U
    3] a basis for W[tex]\cap[/tex]U


    1]
    since i only have limitations on x1 and x4 i call x2=t x3=s x1=x4=q

    therefore W=sp{(1,0,0,1),(0,1,0,0),(0,0,1,0)} and dimW=3

    2]
    to find a basis for W+U, i look for linearly independant vectors that span the space, so i set up a matrix to see which are combinations of the others,
    i got W+U=sp{(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1)}

    these 4 span the whole of R4 so does this mean that W+U = R4
    3]
    to find a basis of W[tex]\cap[/tex]U, i found a homogenic system for each subspace and compared the 2.
    taking a random vector (a b c d) in the subspace, i get
    for W==> -4a+b+3c-sd=0
    for U==> a-d=0
    from the combination i get -6a+b+3c=0
    a=t b=6t-3s c=s d=t

    and so i get W[tex]\cap[/tex]U=sp{(1,6,0,1)(0,-3,1,0)} dim=2
    ----------------------------------------

    does this all look okay,
    also, if i am asked to find a basis and i write the span, is it the same thing, or must i write just one possible basis in the span
     
    Last edited: Jan 27, 2009
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: Linear algebra
Loading...