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- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/04%3A_Determinants/4.01%3A_Determinants-_DefinitionThis page provides an extensive overview of determinants in linear algebra, detailing their definitions, properties, and computation methods, particularly through row reduction. It emphasizes the sign...This page provides an extensive overview of determinants in linear algebra, detailing their definitions, properties, and computation methods, particularly through row reduction. It emphasizes the significance of row operations, such as swaps and scaling, and introduces concepts like triangular matrices and multilinearity. Key properties include conditions for invertibility, the relationship between determinants of products, transposes, and the implications of zero determinants.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/03%3A_Determinants/3.03%3A_Application_of_the_Determinant_to_Inverses_Cramer's_Rule/3.3E%3A_Exercises_for_Section_3.3This page outlines exercises on matrix operations, including determining invertibility via determinants, calculating adjugates and inverses, and using Cramer’s Rule for solving equations. It reveals t...This page outlines exercises on matrix operations, including determining invertibility via determinants, calculating adjugates and inverses, and using Cramer’s Rule for solving equations. It reveals that matrix A is invertible, while matrix B is not, highlighting the role of determinants in unique solutions. Practical applications in electrical circuits are discussed along with challenges addressing numerical stability and conditions for unique solutions.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/02%3A_Matrices/2.04%3A_LU_Factorization/2.4E%3A_Exercises_for_Section_2.4This page features exercises focused on \(LU\) factorizations of various matrices, showcasing the decomposition process into lower and upper triangular forms. It includes solving systems of linear equ...This page features exercises focused on \(LU\) factorizations of various matrices, showcasing the decomposition process into lower and upper triangular forms. It includes solving systems of linear equations through \(LU\) factorization, detailing intermediate steps and solutions.
