1. The problem statement, all variables and given/known data Construct an isomorphism from a 2 by 2 symmetric matrix to R^3. 2. Relevant equations N/A 3. The attempt at a solution I know that for a transformation to be an isomorphic, it must be one-to-one and onto. Would the transform be T:A->R^3 and I would have to choose a general matrix A to test? How would I test it not knowing how the transform is mapped?