is there a transformation which follows these rules:

T: ->

T(-1,1,0,1)=(1,-1,2,1)

T(1,1,1,0)=(2,3,1,-1)

T(-1,5,2,3)=(3,7,0,-3)

ImT is defined as span of the base of the images

so i found that this group is dependant

{(1,-1,2,1),(2,3,1,-1),(3,7,0,-3)}

so ImT=Sp{(1,-1,2,1),(2,3,1,-1)}

so dim ImT=2 and dim kerT=2

so i took basis

and defined T as:

T(-1,1,0,1)=(1,-1,2,1)

T(0,2,1,1)=(0,5,-3,-3)

T(0,0,1,0)=(0,0,0,0)

T(0,0,0,1)=(0,0,0,0)

is it ok?