You mean "linear transformation"- you make a general transformation that does anything!

You mean "set". In "mathematical" English, "group" has a very specific meaning that is not correct here.ImT is defined as span of the base of the images

so i found that this group is dependant

Note that {(-1, 1, 0, 1), (1, 1, 1, 0), (-1, 5, 2, 3)} are{(1,-1,2,1),(2,3,1,-1),(3,7,0,-3)}alsodependent. We can write

-3(-1, 1, 0, 1)+ 2(1, 1, 1, 0)= (-1, 5, 2, 3).

Is T(-1, 5, 2, 3)= -3T(-1, 1, 0, 1)+ 2T(1, 1, 1, 0)?

I don't understand what you mean by this.so ImT=Sp{(1,-1,2,1),(2,3,1,-1)}

so dim ImT=2 and dim kerT=2

so i took basisWhatdid you take as the basis? Are you referring to the standard basis?

Well, you haven't answered the question! What is your answer?[tex]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?