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- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/07%3A_Vector_Spaces/7.04%3A_Linear_Independence/7.4E%3A_Exercises_for_Section_7.4This page discusses exercises on linear independence of vectors and polynomials. It concludes that a specific set of polynomials is linearly independent, while another set is determined to be linearly...This page discusses exercises on linear independence of vectors and polynomials. It concludes that a specific set of polynomials is linearly independent, while another set is determined to be linearly dependent with a provided linear combination. Additional exercises examine conditions for independence in polynomial collections and propose proof methods for assessing the independence of three polynomials in a given space.
- https://math.libretexts.org/Bookshelves/Analysis/Supplemental_Modules_(Analysis)/Ordinary_Differential_Equations/3%3A_Second_Order_Linear_Differential_Equations/3.6%3A_Linear_Independence_and_the_WronskianThis is a system of two equations with two unknowns. The determinant of the corresponding matrix is the Wronskian. Hence, if the Wronskian is nonzero at some t0 , only the trivial solution exists. Hen...This is a system of two equations with two unknowns. The determinant of the corresponding matrix is the Wronskian. Hence, if the Wronskian is nonzero at some t0 , only the trivial solution exists. Hence they are linearly independent.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/02%3A_Systems_of_Linear_Equations-_Geometry/2.05%3A_Linear_IndependenceThis page covers the concepts of linear independence and dependence among vectors, defining linear independence as having only the trivial zero solution in equations. It outlines criteria for testing ...This page covers the concepts of linear independence and dependence among vectors, defining linear independence as having only the trivial zero solution in equations. It outlines criteria for testing independence, including the role of pivot columns in matrices, and explains scenarios where vectors are dependent, such as scalar multiples and inclusion of the zero vector.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/04%3A_R/4.05%3A_Linear_IndependenceThis section discusses the linear dependence and independence between vectors.
