T: R3 – – R3 , T(x,y,z) =(x-y, 2y, x+3z)

T: R³ – – R³ , T(x,y,z) =(x-y, 2y, x+3z) is defined linear transformation. For R³ , S₁= { (1,0,0) , (-1,1,2) , (3,2,0) } and S₂ = { (1,1,0) , (0,1,0) , (0,1,1) } bases. A is represent matrix (T) from S₁ to S₁ , and B is represent matrix from S₂ to S₂. 

a)Find the CekT , GörT , Boy(CekT) , Boy( GörT) . (I couldn’t translate these but i know some infos . 

Cek T = { x ∈ V |T(x) = 0 } So CekT is a subspace.  GorT is a subspace too. )

b) CekT and rank(T) , solve that T is one on one and onto function.

c)Find the A and B.

d) B= X.A.Y so find the X and Y matrixes.