Videos for Matrix Algebra for Engineers (Camosun Math 251)

These videos will help you review some of the basic concepts in the course.
You can view the videos on YouTube or download to your desktop/laptop/tablet.

1.1 Intro to Vectors (2 mins)       Download
1.1 Intro to Linear Combinations (4 mins)       Download
1.2 A Proof about The Dot Product (5 mins)       Download
1.2 Scaling Vectors (4 mins)       Download
1.3 General and Normal Form (3 mins)       Download
1.3 Vector and Parametric Form (6 mins)       Download
1.3 Distance Between a Point and a Line (9 mins)       Download

Cross Product: Equation of a Plane Through Three Points (6 mins)       Download
Cross Product: Area of a Triangle in 3-d (4 mins)       Download
Determinants: Area of a Parallelogram in 2-d (3 mins)       Download
Determinants: Volume of a Parallelepiped in 3-d (9 mins)       Download

2.2 Gaussian Elimination (12 mins)       Download
2.2 Gauss-Jordan Elimination (13 mins)       Download
2.3 Span (7 mins)       Download
2.3 Linear Independence (11 mins)       Download

3.1 Matrix Operations (9 mins)       Download
3.1 Powers of a Matrix (10 mins)       Download
3.2 Span of a Set of Matrices (12 mins)       Download
3.2 A Proof about the Transpose (3 mins)       Download
3.3 The Inverse of a Matrix (8 mins)       Download
3.3 Elementary Matrices (10 mins)       Download
3.4 LU Factorization (8 mins)       Download
3.4 Solving using LU (6 mins)       Download
3.5 Subspaces (9 mins)       Download
3.5 Rowspace, Columnspace and Nullspace (8 mins)       Download
3.6 Standard Matrix of a Linear Transformation (8 mins)       Download
3.6 Image Under a Linear Transformation (7 mins)       Download

4.1 Eigenvalues and Eigenvectors (9 mins)       Download
4.1 The Geometry of Eigenvectors (7 mins)       Download
4.2 Cramer's Rule (7 mins)       Download
4.2 The Adjoint Formula for an Inverse Matrix (7 mins)       Download
4.3 Geometric Multiplicity (6 mins)       Download
4.3 Algebraic Multiplicity (13 mins)       Download
4.3 A Proof about Eigenvectors (5 mins)       Download
4.4 Diagonalization (7 mins)       Download
4.4 Powers of a Matrix and Diagonalization (8 mins)       Download

5.1 Calculations with an Orthogonal Basis (3 mins)       Download
5.1 Orthogonal Matrices (4 mins)       Download
5.2 Orthogonal Complements (7 mins)       Download
5.2 Orthogonal Decompositions (8 mins)       Download
5.3 The Gram-Schmidt Process (7 mins)       Download
5.3 QR Factorization (9 mins)       Download
5.4 Orthogonal Diagonalization (11 mins)       Download
5.4 The Spectral Decomposition (6 mins)       Download

7.3 Least Squares Approximation (8 mins)       Download

Appendix C: The Algebra of Complex Numbers (3 mins)       Download
Appendix C: Complex Eigenvalues and Eigenvectors (12 mins)       Download