I am trying to write a syllabus for a linear algebra course and I wanted to start with a set of questions that a first linear algebra course should address. So far I have the following which I think should be answered regarding linear systems: • Are there any solutions? • Does the system have no, unique or an infinite number of solutions? • How can we find all the solutions if they exist? • Is there some sort of structure to the solutions? Are there any questions we tend to answer on a linear algebra course?