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Homework Help: Linear algebra: Kernel/range

  1. Mar 17, 2013 #1
    1. The problem statement, all variables and given/known data

    Determine the kernel/range of each of the following linear operators on R3


    2. Relevant equations

    3. The attempt at a solution

    So first thing I did was create a 3x1 matrix filled with ones.

    I equaled it to zero and found x1=0 to be a solution. However I'm not quite sure how they come up with the following answer.

    (0,x2,x3). Also why would it be a 2 dimensional subspace? Would it be due to x1 being zero?

    Last edited by a moderator: Mar 17, 2013
  2. jcsd
  3. Mar 17, 2013 #2


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    x1 = 0 if and only if the vector is of the form (0,x2,x3). The subspace spanned by vectors of this form has dimension 2 because for example {(0,1,0), (0,0, 1)} is a basis.
  4. Mar 17, 2013 #3
    Perfect explanation. Thank you!
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