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Linear algebra can be thought of both as the study of vectors and matrices and as the study of linear transformations on an abstract vector space. Both are useful.
I took linear algebra in high school and studied it further in college. I have experience both in the practical nuts and bolts side of matrices and their manipulations as well as the more theoretical end.
I have a AB in Mathematics from the University of Chicago and an SM in Mathematics from the Massachusetts Institute of Technology. I received an award for the best undergraduate record in mathematics and I have taken several graduate courses in logic, including Computability Theory and Model Theory. I have also been teaching and tutoring math for the last 13 years.