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Is T(x,y) = (x,0) a linear transformation

  1. Jan 22, 2008 #1
    1. The problem statement, all variables and given/known data

    I have to determine whether the following is a linear transformation


    2. Relevant equations

    3. The attempt at a solution

    again, let v=(v1, v2) and w=(w1,w2)

    then, T(v+w)=T(v1+w1, v2+w2)=(v1+w1, 0)

    and, T(v)+T(w)=(v1+w1, 0)
    so the first condition holds.


    let c be a constant:
    T(cv)=T(cv1,cv2)=(cv1, 0)=c(v1,0)=cT(v)
    so both conditions hold
    therefore it's linear transformation
    is that correct?
  2. jcsd
  3. Jan 22, 2008 #2


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    Staff Emeritus
    Science Advisor

    You haven't said what x and y are! If they are real numbers, that is that T is a function from R2 to R2, then yes, those are exactly what you need to show. (Of course, taking c= 0 in the second shows T(0)= 0 and taking c= -1 shows T(-v)= -T(v) which are required by not necessary to prove separately.)
  4. Jan 22, 2008 #3
    yea it is

    edit: nevermind listen to halls, you do need to be more precise with this kind of thing probably
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