Linear Algebra
SAI UNIVERSITY FALL 2023
SAI UNIVERSITY FALL 2023
Please click the above link to know when assignments are due and when tests will take place.
Homework:
Assignment 1 (due on Monday, 4 September) Solutions
Assignment 2 (due on Wednesday, 20 September) Solutions
Assignment 3 (due on Wednesday, 18 October) Solutions
Assignment 4 (due on Wednesday, 15 November) Solutions
Problems for determinants, eigenvalues&eigenvectors, Solutions
REVISED FINAL EXAM details
Date: 14 February 2024 (how romantic!)
Time: 10:00 a.m. to 1:00 p.m.
Syllabus: See last page of Lecture 24
Class notes:
Lecture 1: Intro, linear sysems, solution(s) of a linear system
Lecture 2: Augmented matrix, echelon forms, elementary row operations
Lecture 3: Gaussian elimination algorithm, solving a linear system in echelon form
Lecture 4: An example of RREF, applications to network flow, economics
Lecture 5: Application to chemistry, towards inverse of a matrix
Lecture 6: Elementary matrices, computing inverses using Gaussian elimination
Lecture 7: Inverses of elementary matrices, LU decomposition
Lecture 8: Complexity of the Gaussian elimination algorithm, comparisons, Vector spaces intro
Lecture 9: Subspaces, examples, Column and Null space of a matrix
Lecture 10: Linear Independence of vectors, examples, rank of a matrix
Lecture 11: Basis and dimension of a vector space/subspace
Lecture 12: Linear transformations
Lecture 13: Matrix of a linear transformation, solved examples
Lecture 14: Using matrices for computer graphics in R^2
Lecture 15: Kernel and Range, Rank-Nullity Theorem
Lecture 16: Injective and surjective linear maps, Inner Product spaces
Lecture 17: Orthogonal vectors, orthogonal complements, orthogonal sets
Lecture 18: An application of orthogonality to pattern recognition
Lecture 19: Orthogonal projections, Gram-Schmidt process
Lecture 20&21: QR factorization, least-squares approximation
Lecture 22: Determinants
Lecture 23: Eigenvalues, Eigenvectors
Lecture 24: Diagonalizability, final exam info