Linear Combinations: Vectors and Matrices

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Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

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

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Covers linear applications, matrices, transformations, and the principle of superposition.

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

Explores matrices, inverses, and their applications in linear algebra, emphasizing composition and transformation properties.

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Explores linear combinations, matrix-vector product, and matrix equation solutions.

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