These are slides from the SMART Podium used in class.
Lesson 1: This lecture discussed material from Section 2.1 of Lay’s Linear Algebra. Here are a list of key concepts in this material linked to their respective Wikipedia articles: matrices, scalar multiplication, matrix addition, the zero matrix, matrix multiplication, the identity matrix, the transpose of a matrix.
Lesson 2: This lecture continued from lesson 1 covering operations listed there that the lecture did not touch upon. In addition to these the notion of vector was introduced from Section 1.3 of Lay. Here are the topics: column vectors, vectors, vector addition, scalar multiplication.
Lesson 3: This lesson introduced elementary row operations and their elementary matrices. This is motivated by solving a system of linear equations. Augmented and coefficient matrices are contrasted. Here are topics linked: elementary row operation, elementary matrices, system of linear equations, augmented matrix, coefficient matrix.
Lesson 4: This lesson covers the algebraic properties of partitioned matrices and introduces linear combination and linear independence. An example is given using RGB coloring at http://drpeterjones.com/colorcalc/.
Lesson 5: This lesson connects pivot positions to linear independence through homogeneous systems of linear equations.
Lesson 6: This lesson illustrates that every linear transformation has a standard matrix.
Lesson 8: This lesson connects invertiblity of a linear transformation to bijectiveness, and to the invertibility of the standard matrix.
Lesson 9: This lesson demonstrates how one can use row reduction and partitioned matrices to test invertibility of a matrix while simultaneously computing its inverse, if it is. The example is worked out in the notes for section 1594.
Lesson 10: Subspaces and Bases 1: this lesson introduced the notion of a subspace of Rn and two examples, the null space of a matrix and the column space of a matrix. It also introduced the notion of a basis of a subspace.
Lesson 11: Subspaces and Bases 2: an example of how a to construct the basis of the null space and the column space of a matrix by solving its associated homogeneous system of equations.
- Lesson11-1594&6642: These notes were typed up in advance in MS Word and exported to .pdf format.
Lesson 13: Introduction to determinant: This lesson introduces the determinant of a matrix as a product of the distortion of volume and the sign of the effect on orientation.
Lesson13.5: A nice proof that the parity of a permutation is well-defined.
Lesson 14: Computing determinants: This lesson introduces facts about determinants of triangular matrices and transposes of matrices. Co-factor expansion is introduced and determinants of 2-by-2 matrices is reviewed.
