The professor is teaching one section of a class where different sections are taught by different faculty. As all the students - regardless of which section they are enrolled in - are enrolled in the same course, they should all be studying the same material.
Yeah, and that's common. The department says that a linear algebra course should cover a list of selected topics: systems of equations, matrix algebra, vector spaces, etc. But it is straight-up stupid to require professors to all teach the same material in the same order from the same textbook the same way. The student population benefits from having a variety of perspectives. A lot of problems get solved when two people who learned the same thing in two different ways get together.