Linear Algebra: Matrices and Vector Spaces

Related lectures (24)

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Covers the properties and operations of vector spaces, including addition and scalar multiplication.

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

Explores matrix operations, rank determination, kernel dimensions, and basis concepts in linear algebra.

Explores linear dependence theorems and proofs, emphasizing the importance of understanding linear dependence in linear algebra.

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

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Covers vector spaces, subspaces, kernel, image, linear independence, and bases in linear algebra.

Explores linear combinations, basis determination, and vector space dimensionality through practical examples and exercises.

Explores solutions of linear equations, null spaces, subspaces, vector spaces, linear independence, bases, and dimensions.

Explores linear dependence and independence of vectors, including subspaces generation and corollaries.