The methods of Linear Algebra are used in applications that involve systems of equations to formulate, solve, and understand the solutions. Linear algebra is a fundamental tool in modern applications of mathematics, used to solve many real-world problems, (scheduling flights, ranking webpages in search engines, or modeling fluid dynamics, etc.) This book covers the essential ideas and methods of Linear Algebra and acquaints the reader with how to use the techniques of matrices and vector spaces in solving problems. This book can be used for an undergraduate course on the foundations of Linear Algebra, designed for students in the sciences and engineering. After completing such a course, you should understand fundamental topics of linear algebra including vectors, matrices, linear systems, vector spaces, eigenvalues and eigenvectors, and orthogonality.
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