“How do you solve multiple equations with the same unknowns at the same time? Are there more efficient ways to do this than manipulating and fitting one of the equations into the others? What are matrices and how do you handle them mathematically? Can you add and subtract with them? What makes matrix multiplication different from ordinary multiplications? What are determinants and how can you calculate their value? What does it mean for a set of vectors to be linearly independent? What is the difference between isomorphism and homomorphism?
Are you looking for a textbook in linear algebra that puts equal focus on understanding theory and solving a ton of examples? Perhaps your main interest is in applications of linear algebra, such as Markov chains, accuracy of computation, crystals, paradoxes in voting, magic squares, fitting a model to data, projective geometry, page ranking, coupled oscillators or population biology?”