UPDATE LINEAR ALGEBRA FALL 2023 SITARAMAN

LINEAR ALGEBRA FALL 2023 UPDATE PAGE SITARAMAN

Welcome.
Here you will see info about what we did in class, upcoming exams, solutions for past exams, etc.,
CHECK AT LEAST ONCE A WEEK!!

COURSE PAGE WITH SYLLABUS, GRADING SCHEME, ETC.,

OLD FINAL EXAMS

The textbook comes with a website with practice problems, tutorials etc.,
You can get there by clicking on "Mymathlab and mastering" in canvas. Instructions on how to use it are under announcements in canvas.

Zoom link in case anyone needs to meet with me outside of office hours are on canvas, under announcements. Please email me in advance.

CELL-PHONE AND LAPTOP USE IN CLASS PROHIBITED UNLESS REQUIRED BY INSTRUCTOR

WHAT IS LEARNING MATH ALL ABOUT?

SOLUTIONS FOR ALL QUIZZES AND TESTS from SPRING 2014

EXAMS WILL BE ANNOUNCED BELOW

CLASSROOM CHB 306

12/7/23 Thursday
Please read the solutions below. Grades will be done by Friday and I will be in office Friday until 2pm.
Final exam solutions
Final exam Problems

Final exam on Dec 6 wednesday 5 to 7pm (date for course exams on calendar).
Same room -- if it is locked go to my office.

You can study spring 2014 (all problems) and spring 2011 (all except 11) final exams.

Review monday on zoom 11am to 1pm.

ALL OUTSTANDING ISSUES MUST BE CLEARED BY FRIDAY DEC 1, 4PM.

12/1/23 Monday
Please read the solutions below. No class on wednesday.
Test 3 Solutions
Test 3 Problems

TEST 3 ON DEC 1 FRI. REVIEW IN CLASS NOV 29 WEDNESDAY.
WILL COVER 1.10, 2.9, 3.1 to 3.4, 4.1 to 4.7, 5.1 to 5.4.
Please study class notes, review problems posted here, and practice problems.
Also try Spring 2014 Test 3 and Spring 2011 Test III and Spring 2009 Test III (except 6,7, and 8), and also try the quizzes 6,7,8 of spring 2011 at the SPRING 2011 AND SPRING 2009 update page
Please try the problems before reading the answers.

11/27/23 Monday
Today we talked about eigenvectors and applications to stochastic processes and markov chains.
(Updated -- refresh) Notes for today on vector spaces.
Please study relevant parts of 5.6.
Practice problems:
5.6: 1, 3.

11/20/23 Monday
Please read the solutions below. No class on wednesday.
Quiz 9 Solutions
Quiz 9 Problems

QUIZ 9 on monday, on 4.7, 5.1, 5.2, 5.3, 5.4. If you read the notes given below and do the practice problems you should be fine.
11/17/23 Friday
Today we talked about eigenvectors, change of basis, and diagonalization.
(Updated -- refresh) Notes for today on vector spaces.
Please study relevant parts of 4.7, 5.3 and 5.4.
Practice problems:
4.7: 5, 7, 13
5.3: 5, 7, 11, 21, 22
5.4: 5, 13, 18-23
5.1: 1, 5, 9, 13, 21, 22, 31, 32.
5.2 1, 5, 9, 11, 15.

11/15/23 Wednesday
Today we talked about eigenvalues and eigenvectors.
(Updated -- refresh) Notes for today on vector spaces.
Please study relevant parts of 5.1 and 5.2
Practice problems:
5.1: 1, 5, 9, 13, 21, 22, 31, 32.
5.2 1, 5, 9, 11, 15.

11/13/23 Monday
Please read the solutions below. We will finish chapter 4 (vetor spaces) on wednesday.
Quiz 8 Solutions
Quiz 8 Problems

QUIZ 8 on monday, 11/13, on 3.2, 3.3, 4.1 to 4.6.
If you read the notes given below and do the practice problems you should be fine.
11/8/23 Wednesday
Today we talked about basis and dimension for vector spaces and subspaces.
Notes for today on vector spaces.
Please study relevant parts of 4.2 to 4.6
Practice problems:
3.2: 33 to 39.
3.3: 1, 3, 5.
4.1: 1, 5, 6, 11, 15,21, 23, 24.
4.2: 1, 5, 7, 11, 13, 23, 25, 26.
4.3: 1, 3, 13, 21 4.4: 1, 3, 5, 7, 13 4.5: 1, 3, 9, 11, 19 4.6: 1, 5, 9, 17, 18

11/6/23 Monday
Today we talked about determinants of matrix products, Cramer's rule, and vector spaces and subspaces.
Please study relevant parts of 3.2, 3.3, 4.1 and 4.2.
Practice problems:
3.2: 33 to 39.
3.3: 1, 3, 5.
4.1: 1, 5, 6, 11, 15,21, 23, 24.
4.2: 1, 5, 7, 11, 13.

11/3/23 Friday
Please read the solutions below. We will start chapter 4 (vetor spaces) on monday.
Quiz 7 Solutions
Quiz 7 Problems

11/1/23 Wednesday
QUIZ 7 ON FRIDAY, 1.10, 2.9,, 3.1,3.2,3.3.
That is a lot of stuff but if you try the practice problems you will be fine.
Today we talked about an determinants and their properties.
Please study relevant parts of 3.1, 3.2, 3.3.
Practice problems:
3.1: 1, 3, 7, 9, 33, 35, 36, 37.
3.2: 5, 15, 17, 19, 20, 21, 27, 28.
3.3: 11, 13, 17.

10/30/23 Monday
Today we talked about an application of matrix products, co-ordinates, and determinants of 2 by 2 matrices.
Please study relevant parts of 1.10, 2.9 and 3.1.
Practice problems:
1.10: 9, 11, 12.
2.9: 1, 3, 5, 7.
3.1: 33, 35, 36, 37.

10/27/23 Friday
Please read the solutions below. We will start 3.1 (Determinants) on monday.
Test II Solutions
Test II Problems

TEST 2 ON OCT 27 FRI. WILL COVER 1.6, 1.7, 1.8, 1.9, 2.1, 2.2, 2.3, 2.8, 2.9. REVIEW IN CLASS OCT 25 WEDNESDAY.
Please study all class notes (see below), quiz solutions and practice problems.
Please try : Spring 2014 TEST I (only 4 and 5)
Spring 2014 TEST II
Spring 2011 Test I (only 4 and 6)
and Spring 2011 Test II
Spring 2009 Test I (only 6 and 8- note that 8 is mislabelled as 6)
and Spring 2009 Test II (only 1 and 2, ignore LU factorization)

10/23/23 Wednesday
Today we talked about vector spaces, subspaces, column and null spaces.
Please study relevant parts of 2.8 and 2.9.
Practice problems:
2.8: 3, 5, 7, 15, 17, 21, 22, 23, 25.
2.9: 3, 5, 9, 13, 15, 17, 18, 19.

10/20/23 Monday
Today we talked about pivots, 1-1, onto and invertibility.
Please study relevant parts of 2.2 and 2.3.
Practice problems:
2.3: 4, 5, 7, 11, 13, 15, 17, 33, 35, 36, 37.

10/18/23 Wednesday
FRIDAY CLASS ONLINE DUE TO HOMECOMING!
Please read the solutions below. We will start 2.3 ( properties of inverse of linear transformations) on monday.
Quiz 6 Solutions
Quiz 6 Problems

QUIZ 6 ON WEDNESDAY, 10/18, on 1.9, 2.1, 2.2.
10/16/23 Monday
Today we reviewed linear transformations being onto and one-one and did examples.
We also started on matrix multiplication and matrix inverses (2.1, 2.2).
Notes for 1-1, onto (Pearson notes with added slides)

Please study relevant parts of 1.9, 2.1 and 2.2.
Practice problems for today -- 1.9: see friday update below.
2.1: 3, 9, 10, 15, 27.
2.2: 1, 5, 8, 9, 25, 31.

10/13/23 Friday
Today we talked about conditions for linear transformations being onto and one-one.
Notes for today (Pearson notes with added slides)

Please study relevant parts of 1.9.
Practice problems for today -- 1.9: 23, 24, 25, 27, 31, 32, 35, 37, 39.

10/11/23 Wednesday
Today we talked about linear transformations being onto and one-one.
Notes for today (Pearson notes with added slides)

Please study relevant parts of 1.9. No practice problems for today.
Try to find examples of linear transformations that are 1-1 and / or onto.

10/6/23 Friday
Please read the solutions below. We will continue 1.9 ( linear transformations) on monday.
Quiz 5 Solutions
Quiz 5 Problems

QUIZ 5 will be friday, on 1.8 and 1.9.

10/4/23 Wednesday
Today we talked about matrices of linear transformations.
Please study relevant parts of 1.9:
Practice problems:
1.9: 1, 7, 19, 21.

10/2/23 Monday
Today we started linear transformations.
Notes for today (Pearson notes with added slides)

Please study relevant parts of 1.7:
Practice problems:
1.8: 1, 17, 19, 25, 27, 31, 33, 35.

9/30/23 Saturday
Please read the solutions below. We will start 1.8 ( linear transformations) on monday.
Quiz 4 Solutions
Quiz 4 Problems

QUIZ 4 ON FRIDAY, ON 1.6 AND 1.7.

9/27/23 Wednesday
Today we talked about linear independence of vectors.
Please study relevant parts of 1.7:
Practice problems:
1.7: 1, 3, 9, 11, 15, 17, 21, 33.

9/25/23 Monday
Today we started applications of systems of linear equations.
Notes for today (Pearson notes with added slides)

Please study relevant parts of 1.6:
Practice problems:
1.6: 1, 3, 5, 7, 11, 13.

9/22/23 Friday
Please read the solutions below. We will start 1.6 (Applications of linear equations) on monday.
Test I Solutions
Test I Problems

TEST I ON FRIDAY SEP 22. REVIEW IN CLASS SEP 20 WEDNESDAY.
Please study all class notes (see below), quiz solutions and practice problems.
Please try Spring 2014 TEST I (all except 4 and 5) Also try Spring 2011 Test I (all except 4 and 6) and Spring 2009 Test I (all except 6 and 8)

9/18/23 Monday
Today we continued talking about matrix equations and also talked about homogenous equations and parametric solutions.
Please study relevant parts of 1.5
Practice problems:
1.5: 3, 5, 7, 11, 23, 25.

9/13/23 Wednesday
NO CLASS FRIDAY.
Please read the solutions below. We will start 1.5 (solution sets of linear equations) on monday.
Quiz III Solutions
Quiz III Problems

QUIZ 3 ON WEDNESDAY. COVERS 1.3 AND 1.4
9/11/23 Monday
Today we continued talking about vector equations and linear combinations and also started talking about matrix equations.
Notes for today (Pearson notes with added slides)

Please study relevant parts of 1.3 and 1.4
Practice problems:
1.3: 1, 3, 5, 7, 9, 11, 13, 23.
1.4: 5, 7, 11, 23, 25.

9/8/23 Friday
Today we started talking about vector equations and linear combinations.
Notes for today (Pearson notes with added slides)

Please study relevant parts of 1.3.
Practice problems:
1.3: 1, 3, 5, 7, 9, 11.

9/6/23 Wednesday
Please read the solutions below. We will start 1.3 (vector equations) on friday.
Quiz II Solutions
Quiz II Problems

Next quiz on wednesday, based on 1.2.

Friday, 9/1/2023
Today we talked more about finding solutions of a system of linear equations by making the augmented matrix into reduced echelon form and looking at the pivot positions.
(PLEASE REFRESH) Notes (Pearson notes with added slides) Using reduced echelon matrix for solving systems
Please study all practice problems from 1.2 (5th edition of Lay's book) assigned so far, to prepare for quiz on wednesday.

Wednesday, 8/30/2023
Today we saw how to find solutions of a system of linear equations by making the augmented matrix into reduced echelon form and looking at the pivot positions.
Notes (Pearson notes with added slides) Using reduced echelon matrix for solving systems
Please try problems 15, 17, and 23 from 1.2 (5th edition of Lay's book). Also try the problems from friday by getting reduced echelon matrix.

8/28/23 Monday
Quiz I Solutions
Quiz I Problems

QUIZ 1 WILL BE MONDAY, ON 1.1 AND (PART OF) 1.2.

Friday, 8/25/2023
Today we saw how to find solutions of a system of linear equations by making the augmented matrix into echelon form.
Please also read about reduced echelon form in textbook: only additional thing is leading nonzero elements should equal 1 and the entries above those should also be zero.
Notes (Pearson notes with added slides) Basic definitions and steps for solving systems
Please try problems 1, 3, 7, 11 from 1.2 (5th edition of Lay's book). You can solve them by stopping at echelon matrix as well, without getting reduced echelon form.

Wednesday, 8/23/2023
Today we talked about what kind of solutions a system of linear equations have and how to obtain them using matrices and row operations.
Notes (Pearson notes with added slides) Basic definitions and steps for solving systems
Please try problems 1, 3, 5, 7, 11, 15, 29 from 1.1 (5th edition of Lay's book)

Tuesday, 8/22/2023
Yesterday we talked about application of linear algebra (and math in general) to making animation in movies and video games.
Check out this movie Math and movies -- by Numberphile
We went through the basic meaning and purpose of linear algebra.
I have posted a Zoom link in case anyone needs to meet with me outside of office hours are on canvas, under announcements. Please email me in advance.
The textbook comes with a website with practice problems, tutorials etc., You can get there by clicking on "Mymathlab and mastering" in canvas. Instructions on how to use it are under announcements.

8/17/2023
Spring 2014 Final Exam Solutions
Solutions and Comments for Final exam

LINEAR ALGEBRA AND COMPUTER GRAPHICS-- A VERY BRIEF INTRODUCTION
I encourage you to explore more -- just google the various terms used in this presentation-- especially "Polygonal Mesh" and "Motion Capture."
Updated 8/17/2023