1. The problem statement, all variables and given/known data Let T be a linear transformation from R3 to R3. Suppose T transforms (1,1,0) ,(1,0,1) and (0,1,1) to (1,1,1) (0,1,3) and (3,4,0) respectively. Find the standard matrix of T and determine whether T is one to one and if T is onto 2. Relevant equations 3. The attempt at a solution I know T(x) =Ax=[T(e1) ,T(e2,) T(e3)] I thought A would just be the matrix with columns (1,1,1) (0,1,3) and (3,4,0), but then I realized that (1,1,0) ,(1,0,1) and (0,1,1) are not the standard basis vectors for R3 My book doesn't give any examples where we don't start with the standard basis vectors Should I have started by taking a 3x3 matrix entries [x1,x2,x3;x4,x5,x6] and multiply that by a 3x3 matrix with entries [1,1,0;1,0,1;0,1,1] and set that equal to a matrix with entries [1,0,3;1,1,4;1,3,0] and then got a system of equations from there by multiplying the left side out. And then set up an augmented matrix and used row reduction to find corresponding entries for A?