The basis of linear algebra was established since the linearity was known in the early 17th century, the determinant was introduced in the 18th century, and the concept of vector, vector space and matrix was completed in the 19 century. The linear algebra plays an important role with the differential and integral in the mathematical application. This paper is suggested for the application of linear algebra to the mathematical education. The quadratic curve is demonstrated in terms of the matrix on the plane by using the orthogonal transformation in vector space R2 on the real field and various kinds of shapes are classified according to the graph.