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This lecture introduces the fundamental concepts of linear algebra and its applications in various fields such as image processing, signal analysis, and genetics. The course covers theoretical foundations, practical algorithms, and weekly quizzes and exercises to reinforce learning. The instructors provide detailed corrections and strategies for solving complex problems, focusing on topics like inner product spaces, orthogonal matrices, and symmetric matrices. Linear algebra is highlighted as a key subject for engineers and mathematicians, offering a gateway to diverse high-level applications.