Gaussian Elimination Method

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Covers linear equations, systems of linear equations, and matrices, including Gaussian elimination.

Covers elementary row operations, row-equivalent matrices, row-echelon form, Gauss method, uniqueness of reduced form, and matrix rank.

Focuses on transforming linear systems into triangular matrices to simplify the process of finding solutions.

Explores solving systems of equations with parameters to find different types of solutions.

Covers matrix notation for linear equations, solutions, and geometric interpretations.

Explores the equality of row spaces for equivalent row matrices and the determination of row ranks.

Covers LU factorization, determinants, subspaces, and matrix products.

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Covers matrix invertibility, determining if a matrix is invertible, calculating its inverse, and elementary matrices.

Covers strategies for calculating determinants and their geometric interpretation in various dimensions.