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This is the first course of a three course specialization that introduces the students to the concepts of linear algebra, one of the most important and basic areas of mathematics, with many real-life applications. This foundational material provides both theory and applications for topics in mathematics, engineering and the sciences. The course content focuses on linear equations, matrix methods, analytical geometry and linear transformations. As well as mastering techniques, students will be exposed to the more abstract ideas of linear algebra. Lectures, readings, quizzes, and a project all help students to master course content and and learn to read, write, and even correct mathematical proofs. At the end of the course, students will be fluent in the language of linear algebra, learning new definitions and theorems along with examples and counterexamples. Students will also learn to employ techniques to classify and solve linear systems of equations. This course prepares students to continue their study of linear transformations with the next course in the specialization. .