About Vectors | Chapter 1, Essence of linear algebra

Cramer's Rule: A Geometric Interpretation via Determinants and Volume Scaling Dot Products and Duality: Vectors as Linear Transformations Physics Computing 2x2 Matrix Eigenvalues from Trace and Determinant Cross Product Geometry via Dual Vectors and Determinants Linear Transformations of 3D Vectors via Matrix Representations Mathematics in general Mathematics for nonmathematicians (engineering, social sciences, etc.)