Determinant, Area and Volume

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Explores linear applications, matrices, transformations, rotations, symmetries, and properties of applications.

Explores linear applications, matrices, injectivity, surjectivity, and compositions of linear maps with examples and demonstrations.

Covers matrix rank, determinant, and decomposition in linear algebra.

Explores the geometric interpretation of determinants in linear algebra, emphasizing area and volume calculations.

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Explores determinants, similarity invariance, Cramer's formula, and geometric interpretations in matrices.

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

Covers examples of 3x3 matrix representations and their geometric interpretations.

Explores properties of orthogonal and triangular matrices with linearly independent columns and their mathematical operations.