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This looks like a standard “Discrete Mathematics” course, or an “Introduction to Proofs” type course, where the style is definition-theorem-proof. If linear algebra were to be introduced in this class, then it would likely be at a theoretical level where linear algebra would be introduced through definition-theorem-proofs, starting with proving trivial things like (−1)v=−v.

It would probably take an entire semester to get to more advanced topics in linear algebra. This is typically its own course and isn’t the computational version.

Despite the book’s title this course is more geared towards getting students ready for Algorithms and other CS theory level courses.