Did these courses include introduction to proof techniques and practice with such? Discrete math often does, but the level of such can vary. College sophomore level linear algebra is often more computationally focused, unless it is an honors or more theory focused version.
As noted above, the UCB math department recommends a college junior level linear algebra course (with more focus on theory and proofs than college sophomore level courses) as the first upper level math course, rather than jumping into real analysis first.