Linear Algebra is one of the most foundational areas of modern mathematics, widely valued by scientists and engineers for its diverse and powerful applications. Rather than focusing solely on manual computations—something that first-time learners may emphasize, as they often have in other math classes—linear algebra encourages a deep understanding of concepts and structures. While solving problems by hand is a useful exercise, large-scale computations are typically handled by computers. This conceptual approach is crucial for leveraging linear algebra in both practical applications and theoretical explorations. Moreover, linear algebra serves as a gateway to modern algebra, also known as abstract algebra, which provides a "common language" across various branches of mathematics. For enthusiasts of pure mathematics, studying linear algebra offers an excellent introduction to the broader world of contemporary mathematical thought.