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Lesson 12: Linear Independence
The document covers concepts of linear independence and rank in the context of vector spaces, highlighting when vectors are considered dependent or independent based on their coefficients. It provides examples and definitions, emphasizing the relationship between linear independence and matrix invertibility. Key exercises and solutions illustrate the process of determining linear relationships among sets of vectors.
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Overview of Lesson 12 including problem set assignments and midterm exams.
Definition of linear dependence, conditions for vectors to be dependent or independent.
Examples of determining linear independence in vector sets using equations and solutions.
Connection of linear independence with invertibility of matrices and absence of dependence relations.
