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Related lectures (31)
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Linear Systems: Solutions Study
Covers the study of solutions of linear systems through elementary operations.
Solving the linear system: Direct methods
Covers the process of solving a linear system in numerical flow simulation using direct methods like Gaussian elimination and the TDMA algorithm.
Matrix Equivalence and Reduced Row Echelon Form
Explores matrix equivalence, consistency, row generation, and reduced row echelon form implications.
Method Summary, Homogeneous Systems
Summarizes the method for solving homogeneous systems of linear equations and discusses their properties and solutions.
Simplex Algorithm: Pivoting
Covers the simplex algorithm, pivoting, elementary row operations, and transformations to find matrix Q.
Rank Revisited: Line and Column
Revisits line and column ranks in matrices, demonstrating their equality and properties.
Linear Systems: Direct Methods
Explores linear systems, Gaussian elimination, LU decomposition, and matrix types.
Reduced Echelon Matrices: Properties and Uniqueness
Explores the properties and uniqueness of reduced echelon matrices and the criterion of invertibility.
Direct Methods for Linear Systems of Equations
Explores direct methods for solving linear systems of equations, including Gauss elimination and LU decomposition.
Matrix Computations: Complexity and Algorithms
Explores matrix computation complexity, known algorithms, and structured solvers' impact.