"Linear algebra"is a compulsory public basic course for science and technology majors in undergraduate universities.It has the characteristics of abstract theory,strict logic and complex calculation.In order to implement the student-centered teaching concept under the background of new engineering,this paper explores the teaching design and practice of"linear algebra"based on the BOPPPS model to realize the organic combination of knowledge education and ideological and political education,and further improve students'mathematical professional ability,aiming at the problems of"linear algebra"teaching with fewer hours and heavier tasks and heavier derivation than application.It can also effectively cultivate students'ideological and political quality and social responsibility.