1. Limited time only! Sign up for a free 30min personal 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-solution space

  1. Feb 2, 2013 #1
    1. The problem statement, all variables and given/known data
    a)Let M be a m*n matrix and x be a n*1 coordinate vector. How can you check whether or not x is in the solution space of M?

    [0 1 1 1 0]
    M=[1 1 0 0 1]
    [0 1 1 0 1]
    [1 0 1 0 0]

    b)To decide whether or not the following are in the solution space of M
    i) v1=[1 0 0 1 1]T ii) v2=[1 0 0 1 1]T
    *T means the transpose of the matrices

    Any help is appreciated


    2. Relevant equations

    {x[itex]\in[/itex]ℝn:Ax=0}

    3. The attempt at a solution

    I started by solving the homogeneous linear equation:
    M*v1=0

    [0 1 1 1 0]
    [1 1 0 0 1]*[0 1 0 1 1]T = 0
    [0 1 1 0 1]
    [1 0 1 0 0]

    [2 2 2 0]T ≠ 0

    ∴ v1 is not in the solution space of M

    Am i doing the right here??
     
  2. jcsd
  3. Feb 2, 2013 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What, exactly, was the wording of the question? To ask about the "solution space" of just a matrix, M, makes no sense. We talk about the "solution space" of an equation like "Mx= b" and the answer depends on b as well as M. The solution space of "Mx= 0", with b specfically equal to 0, is the "null space" or "kernel" of matrix M.

    Yes, to determine whether a given vector, x, is in the solution space of Mx= b, simply multiply M and the given x and see if the result is equal to b. Assuming that the problem is really asking whether the given x is in the "null space", so that b= 0, it is immediately clear that the top row times x does not give 0 and so x is not in the null space.

    But I am still concerned about the wording of the question. If it really said "solution space", it is possible that there is some non-zero "b", perhaps given in a previous part of the problem, that you missed.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Linear algebra-solution space
  1. Linear Algebra (Replies: 3)

  2. Linear algebra (Replies: 22)

Loading...