This workbook offers newcomers to their studies a new approach to the extensive material of linear algebra. The book includes detailed solutions for all exercises from the authors' underlying textbook, with selected problems revisited from different perspectives as the understanding of the material evolves. This allows the reader to more easily follow the lecture content and independently work through the learning materials based on the exercises. Fundamental aspects of the field, as well as the internal and external mathematical implications of the results, are also made clearer.