I have this exercise
Define and find the expression of the linear transformation
Information given:
$ T : \Bbb R^5\to \Bbb R^4$
Im T = ⟨(3, -1, 0, 1), (1, 0, 0, 2), (0, 0, 1 -1)⟩
⟨(3,3 0, 0,0)⟩⊂ Ker T
Solve T(⟨(1; 1; 0; 0); (0; 0; 1; 0)⟩) and give a basis.
I have already define the transformation and found the expresion that is T(x,y,z,w,u)=(x-y+z,-x+y,w,x-y+z-w) And T(⟨(1, 1, 0, 0), (0, 0, 1, 0)⟩) that is T(1,1,0,0,0)=(0,0,0,0)
T(0,0,1,0,0)=(1,0,0,1)
But I have a problem giving the basis, is the transformation basis the imagen basis,I don't really undestand what is the problem asking in that part?