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Homework Help: Not sure how to solve this problem ( lin alg.)

  1. Mar 25, 2006 #1
    The question asls:Show that the range of the linear operator defined by the equations:
    W_1=x_1 - 2*x_2 + x_3
    W_2=5*x_1-x_2+3 *x_3
    is not all of R^3, and find a vector that is not in the range.
    Well, we know T
    I augment W
    and we get
    I do Reduce Echelon
    I get zeros on the bottom
    so i get
    k, well, i chose a vector point, (10,5,6)
    i get
    10 != -1
    not sure if this is correct way of solving it.
  2. jcsd
  3. Mar 25, 2006 #2
    If I read your problem correctly, here's a hint. If there is a vector that is not in the range of the transformation, then what does that tell you about the linear dependence or independence of the three equations?
  4. Mar 26, 2006 #3
    we havent covered linear independence yet.
  5. Mar 26, 2006 #4


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    Science Advisor

    WHY did you choose (10, 5, 6) and HOW did you "get 10 != -1"?
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