Linear algebra finds a natural place in the mathematical modelling of realities; thus, its benefits to physical, biological and social sciences cannot be gainsaid. Moreover, the application of linear algebra concepts to suitable systems helps to achieve deeper insights into such systems, and also to make useful generalizations. This book, application of linear algebra, has been written to satisfy the requirement of undergraduate students of mathematics, engineering, physics, actuarial science, statistics, chemistry, economics, and as many as need to apply linear algebra to their studies and research. It is also a very useful tool for students preparing for the SAT2 Mathematics, A- level Cambridge Mathematics and Further Mathematics, and GRE subject test in Mathematics.The book deals with the application of linear algebra to: linear systems of algebraic equations, least-square approximation, conics and quadratic surfaces, Optics, and systems of constant-coefficient linear ordinary differential equations, as well as intermediary topics needed to make the book a coherent whole. In an attempt to make the subject more substantial and less formal, I have provided the reader with enough computational examples, considering the wide range of my intended audience. However, I have also interspersed this material with some rigorous proofs in order to meet the demand of the more advanced reader as abstraction and rigor cannot be totally eliminated from any useful linear algebra textbook.