Results 1 to 4 of 4

Math Help - Null Space of a Matrix

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    128

    Null Space of a Matrix

    Hello everyone.

    The matrix is

    1 1 -1 2
    2 2 -3 1
    -1 -1 0 5

    I calculated the null space of the matrix as

    Span((-1,1,0,0)^T,(-5,0,-3,1)^T)

    Yet the answer is supposedly

    (-1,1,0,0)^T, Span(-5,0,-3,1)^T

    Why can't I express the first as part of the linear combination (i.e. as part of the span)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Mar 2011
    Posts
    118
    Quote Originally Posted by Lord Darkin View Post
    Hello everyone.

    The matrix is

    1 1 -1 2
    2 2 -3 1
    -1 -1 0 5

    I calculated the null space of the matrix as

    Span((-1,1,0,0)^T,(-5,0,-3,1)^T)

    Yet the answer is supposedly

    (-1,1,0,0)^T, Span(-5,0,-3,1)^T

    Why can't I express the first as part of the linear combination (i.e. as part of the span)?
    the answer is simply span( (-1,1,0,0)). Try inputting (-5,0,-3,1) and it comes out as (0,0,10), not (0,0,0)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2009
    Posts
    128
    Shucks! I'm sorry about putting in wrong data, but that 5 in the (3,4) spot should be NEGATIVE five.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,528
    Thanks
    1387
    You get exactly the same result. That matrix row reduces to
    \begin{bmatrix}1 & 1 & -1 & 2 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 6\end{bmatrix}
    so that (x, y, z, u) will be in the null space if and only if x+ y- z+ 2u= 0, z+ u= 3, 6u= 0. Those last two equations give z= u= 0 and the first equation reduces to x+ y= 0 or x= -y. Every vector in the null space is (x, -x, 0, 0)= x(1, -1, 0, 0). The null space is one-dimensional and {(1, -1, 0, 0)} is a basis ((-1, 1, 0, 0) is a multiple of that so it would also be a basis vector.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Question on null space/column space/row space of a matrix
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: December 1st 2011, 01:47 PM
  2. Null space for Matrix with similar columns
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 17th 2011, 02:08 PM
  3. Dimension of null space of two matrix multiplication
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: August 18th 2011, 11:22 PM
  4. Replies: 3
    Last Post: May 26th 2011, 08:42 PM
  5. basis for null space of matrix
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: March 17th 2009, 06:47 PM

Search Tags


/mathhelpforum @mathhelpforum