1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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).
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...