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Linear Transformation R2->R3 with 'zero' vector

  1. Apr 4, 2012 #1
    1. The problem statement, all variables and given/known data
    Is T(X,Y)->(X,Y,1) a linear transformation? where X and Y are defined R2 column vectors.

    2. Relevant equations
    Attempt to prove T(cX+Y)=cT(X)+T(Y)
    Consider T(cx1+y1,cx2+y2)->(cx1+y1,cx2+y2,1)

    3. The attempt at a solution
    RS=cT(x1,y1)+T(x2,y2)->c(x1,y1,1)+(x2,y2,1)
    =(cx1+y1,cx2+y2,1)+(0,0,c)
    =(cx1+y1,cx2+y2,1)+c(0,0,1)
    The 'zero' vector: T(0,0)->(0,0,1)
    therefore T(cx1+y1,cx2+y2)->(cx1+y1,cx2+y2,1)
    and T(X,Y)->(X,Y,1) is a linear transformation.
     
    Last edited: Apr 4, 2012
  2. jcsd
  3. Apr 4, 2012 #2
    zero vectors are only of the form (0,0) and (0,0,0).
     
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