1. The problem statement, all variables and given/known data Prove that there exists only one linear transformation l: R3 to R2 such that: l(1,1,0) = (2,1) l(0,1,2) = (1,1) l(2,0,0) = (-1,-3) Find Ker(l), it's basis and dimension. Calculate l(1,2,-2) 2. Relevant equations 3. The attempt at a solution I still find linear transformations really confusing. Something about the notation and what is being asked, I don't know... The matrix associated to these linear transformations should be a 2x3 right? L=AX where L = linear transformation A = matrix associated to linear transformation X = vector so, (1,1,0) = A*(2,1) (0,1,2) = A* (1,1) (2,0,0) = A*(-1,-3) And there will be ONE matrix that is associated to all of these transformations? If this is correct, how can I find A?