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I'm currently an undergrad, and I have a quick question about taking grad linear algebra: Initially, I took a matrix theory/algebra class (which was called something like Matrix and Linear Transformations and so it covered some parts of linear transformations), and got a C initially, which I then retook and got a B. Later, I took a course that's actually called Linear Algebra (so this is the more legit linear algebra course & covers everything that was covered in matrix theory/algebra class + more linear algebra stuff & is mathematically rigorous, proof based), and got an A. I have an option to take grad linear algebra as an elective, and I was wondering what you guys think, given that even though I got an A in the Linear Algebra course, those bad grades in matrix algebra worry me. (I had some hard time with math in the beginning, but did better as I took harder courses: in fact, I got straight straight As the past three semesters in all math courses including: two sequences of Real Analysis, Topology, Stochastic Process, PDE and Fourier series, and so on.) I would like to be competitive for top schools (20 or higher), so let me know what your thoughts are, thanks for the help!