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- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/01%3A_Systems_of_Linear_Equations-_AlgebraThis page discusses the algebraic study of linear equations, detailing methods for solving them, particularly through row reduction. It explains a systematic approach to solving equations and how to e...This page discusses the algebraic study of linear equations, detailing methods for solving them, particularly through row reduction. It explains a systematic approach to solving equations and how to express solutions in parametric form. The content is organized into sections that build foundational knowledge on linear equations, algorithms for solutions, and solution representation.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/06%3A_Orthogonality/6.01%3A_Dot_Products_and_OrthogonalityThis page covers the concepts of dot product, vector length, distance, and orthogonality within vector spaces. It defines the dot product mathematically in Rn and explains properties lik...This page covers the concepts of dot product, vector length, distance, and orthogonality within vector spaces. It defines the dot product mathematically in Rn and explains properties like commutativity and distributivity. Length is derived from the dot product, and the distance between points is defined as the length of the connecting vector. Unit vectors are introduced, and orthogonality is defined as having a dot product of zero.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/01%3A_Systems_of_Linear_Equations-_Algebra/1.03%3A_Parametric_FormThis page explains parametric form and free variables in solving linear equations. It outlines how to express solution sets using free variables, demonstrating the infinite solutions available when at...This page explains parametric form and free variables in solving linear equations. It outlines how to express solution sets using free variables, demonstrating the infinite solutions available when at least one variable is free. The text also classifies systems of linear equations based on their augmented matrix forms, identifying three scenarios: inconsistent systems with no solutions, unique solutions, and systems with infinitely many solutions due to free variables.