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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

    x y z
    a b c
    d e f

    ........ etc
  2. jcsd
  3. Jan 17, 2009 #2


    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


    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.
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