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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
    W_3=4*x_1+x_2+2*x_3
    is not all of R^3, and find a vector that is not in the range.
    Well, we know T
    T=[1,-2,1;5,-1,3;4,1,2]
    I augment W
    and we get
    T|W=[1,-2,1,W_1;5,-1,3,W_2;4,1,2,W_3]
    I do Reduce Echelon
    I get zeros on the bottom
    so i get
    w_1-W_2+W_3=0
    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

    HallsofIvy

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    Staff Emeritus
    Science Advisor

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