Linear algebra is one of the most important and beautiful branches of mathematics; therefore, being a linear algebra teacher is both a responsibility and a privilege. Linear algebra is particularly challenging and rewarding in study programs where it is not presented merely as a tool for solving problems, but also as a field in which theoretical concepts are introduced. To achieve a deeper understanding of the material, it is very important to encourage students to view linear algebra from multiple perspectives: concrete and abstract, practical and theoretical, algorithmic and investigative, and local and global. In linear algebra, one rarely remains within a single perspective; instead, there is constant juggling between representations and concepts, which fosters a deeper and more connected understanding of the subject. This approach supports the development of mathematical thinking and helps students apply what they learn in new situations, both within mathematics and in other scientific or technical areas. This chapter presents selected experiences and reflections that illustrate these strategies in the study of linear algebra. It also includes historical insights into the development of several fundamental concepts, highlighting the contributions of J. J. Sylvester.