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 Cross Product: Area, Orthogonality, and the Right-Hand Rule Computing 2x2 Matrix Eigenvalues from Trace and Determinant Linear Transformations and Matrices in Two Dimensions Cross Product Geometry via Dual Vectors and Determinants Linear Transformations of 3D Vectors via Matrix Representations Mathematics for nonmathematicians (engineering, social sciences, etc.) Matrix Multiplication as Composition of Linear Transformations