Analyzing the Connection of Linear Algebra: Enhancing Visual Reasoning through Vector Spaces

Abstract

This paper investigates the significant relationship between geometry and linear algebra, emphasizing the ways in which vector spaces and linear transformations improve visual reasoning. I used post positivist paradigm and quantitative research design. For this research, I selected 90 students to represent a sample of math majors who have completed M.Ed. level coursework, obtained employment, and are enrolled in M.Ed. programs at all Tribhuvan University constituent campuses. It looked at how bases, eigenvectors, linear independence, and dimension are interpreted geometrically and emphasizes in what way important these concepts are for comprehending spaces, forms, and transformations. In order to bridge the gap between abstract algebraic theory and intuitive geometric reasoning, the article also described how these ideas make it easier to analyze linear algebra with geometrically.