In 1990, Linear Algebra Curriculum Study Group was formed for the goal to initiate substantial and sustained national interest in proving the undergraduate linear algebra curriculum. And the five recommendations were generated. The one of them is that mathematics departments should seriously consider making their first course in linear algebra a matrix-oriented course. A matrix-oriented linear algebra course should proceed from concrete, and in many cases practical, examples to the development of general concepts, principles, and the concomitant theory that simplifies and clarifies and makes linear algebra so powerful and useful. Also the theoretical status of linear algebra is important as its applicability and its role in computation. So far, I first preview the historic approach of linear algebra centered vector space and matrix algebra. It is essential to improve and develop students\' conceptional framework and to design effective teaching and learning of linear algebra. Also, two approaches in the curriculum of linear algebra course are discussed. The vectorbased course is more formal, theoretical and abstract than the matrix-based course, which is practical relatively. And I observed the historic tendency of the textbooks of linear algebra compare with the curriculum of linear algebra.