Row-echelon and reduced row-echelon matrices

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Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Explores the properties of invertible matrices, including unique solutions and linear independence.

Explains the Gaussian elimination method for solving linear equations through row operations and pivoting.

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

Covers calculations and algorithms for determining the determinant of a matrix, including permuting rows and multiplying by coefficients.

Introduces the Gauss-Jordan method for solving linear equations and explores unique solutions and efficiency comparisons.

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

Explores matrix equations, solutions, properties, and vector spaces in linear algebra.

Introduces elementary row operations on matrices and their applications in solving systems of linear equations.

Covers elementary row operations, equivalent matrices, invertibility, and bases in linear algebra.