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Related lectures (23)

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Explains linear independence, basis, and matrix rank with examples and exercises.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Covers linear independence, bases, and coordinate systems with examples and theorems.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Covers vector spaces, operations, and linear independence with examples from polynomials and functions.

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Explores linear independence in vector spaces and the concept of bases.

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.