Lectures related to Matrix Equations: Linear Combinations and Solutions

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

Covers vector equations, linear combinations, and the span of vectors.

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

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

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

Explores the properties of invertible matrices, including unique solutions and linear independence.

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