Lecture Notes
- Lecture 0 (January 11, 2021)
Linear systems of equations, solutions (0,1 or infinitely many), examples.
- Lecture 1 (January 13, 2021)
Matrices encoding a linear system, elementary operations, echelon form.
- Lecture 2 (January 15, 2021)
Reduced echelon form, Gauss-Jordan elimination.
- Lecture 3 (January 20, 2021)
Consistent/inconsistent systems. Homogeneous systems.
- Lecture 4 (January 22, 2021)
Homogenous systems cntd. Matrices. Addition, scalar multiplication
and matrix multiplication.
- Lecture 5 (January 25, 2021)
Matrix multiplication again.
- Lecture 6 (January 27, 2021)
Formal algebraic properties of matrix operations.
- Lecture 7 (January 29, 2021)
Invertible matrices. Computing matrix inverses.
- Lecture 8 (February 1, 2021)
Linearly independent set of vectors.
- Lecture 9 (part 1) (February 3, 2021)
Linearly dependent and independent vectors again.
- Lecture 9 (part 2) (February 3, 2021)
Vectors in 2 and 3 dimensions. Addition and scalar multiplication.
- Lecture 10 (February 5, 2021)
Vectors in 2 and 3 dimensions. Dot product.
- Lecture 11 (February 10, 2021)
Vectors in 2 and 3 dimensions. Cross product.
- Lecture 12 (February 12, 2021)
Lines and planes.
- Lecture 13 (February 15, 2021)
Subspaces of R^n. Two main examples.
- Lecture 14 (February 17, 2021)
Null space and range of a matrix.
- Lecture 15 (February 19, 2021)
Basis of a subspace. Dimension.
- Lecture 16 (February 22, 2021)
Examples. Rank and Nullity of a matrix.