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Homework Help: Nullity, rank, image and kernel answer check

  1. Dec 27, 2008 #1
    My question is let the linear mapping T : R2->R3 be given by T(x,y)=(x-y,2y-2x,0)

    write down bases for its image and null-space and determine its rank and nullity.
    Find the matrix A that represents T with respect to the standard bases of R2 and R3

    now i think i know how to do this but i'm revising and have no answers and would hate to be revising the wrong things, so can i please have a moment of someones time to confirm this is right, thanks

    firstly A= {(1,-1),(-2,2),(0,0)}

    kernal is when y=x so bases for a kernal is a(1,1) and n(t)=1

    image is b(1,-2,0) r(t)=1

    so r(t)+n(t)=2 as expected
  2. jcsd
  3. Dec 27, 2008 #2


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    Looks ok to me.
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