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 17, 2009 #1
    gven a matrix A=

    1 0 2
    1 1 1
    5 2 8

    and knowing AB=0 ,B[tex]\neq[/tex]0
    what are possible values of B

    is there any way to solve this other than
    making B a matrix of parameters , doing the multiplication and solving, ie
    B=

    x y z
    a b c
    d e f

    x+0a+2d=0
    y+0b+2e=o
    ........ etc
     
  2. jcsd
  3. Jan 17, 2009 #2

    Mark44

    Staff: Mentor

    It's helpful to know about the nullspace of a matrix in this problem. In general, the nullspace is the set of vectors x such that Ax = 0.

    For this problem, the nullspace is one-dimensional, and consists of all scalar multiples of (-2, 1, 1).

    Instead of looking at AB = 0, think about what's happening to the individual columns of B, call them B_1, B_2, and B_3. What can you say about A*B_1 = 0? A*B_2 = 0? A*B_3 = 0?
     
  4. Jan 17, 2009 #3
    all got to be multiples of (-2 1 1)??? am i on the right track, havent yet learned about nullspace.
     
  5. Jan 17, 2009 #4

    Mark44

    Staff: Mentor

    Yes and yes, so congratulations! Keep in mind that the columns are different multiples of (-2, 1, 1). (Hint: use parameters.)

    To check, write a matrix B as above and calculate AB. Should come out with the 3 x 3 zero matrix.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Linear algebra
  1. Linear algebra (Replies: 3)

  2. Linear Algebra (Replies: 5)

  3. Linear Algebra (Replies: 1)

Loading...