The inverted classroom is a course design model in which students' initial contact with new information takes place outside of class meetings, and students spend class time on high-level sense-making activities. The inverted classroom model is so called because it inverts or "flips" the usual classroom design where typically class time is spent on information transfer (usually through lecturing) while most higher-order tasks are done outside the classroom through homework. The inverted classroom model is particularly well-suited for linear algebra, which mixes relatively straightforward mechanical calculation skills with deep and broad conceptual knowledge. In this paper, we discuss how the inverted classroom design can be applied to linear algebra in three modes: as a one-time class design to teach a single topic, as a way to design a recurring series of workshops, and as a way of designing an entire linear algebra course.