Linear Algebra is one of the fundamental courses in college mathematics. According to our experiences, we found that the Input-Output Analysis can be used to motivate students of Linear Algebra. In this paper, we propose a way of teaching Linear Algebra with applications to the Input-Output analysis which is based on our experience of teaching Linear Algebra in recent years. The students in mind are those in economics areas and the course in mind is one which students take for the first time as a Linear Algebra course.