LINEAR ALGEBRA SPRING 2024 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 FALL 2023
 

EXAMS WILL BE ANNOUNCED BELOW

CLASSROOM LKH 208


5/2/24 Thursday
Grades will be posted on bisonweb soon. Please wait for it to appear.

Final exam solutions

Final exam problems


FINAL EXAM MAY 1, WED, 5 TO 7PM. SAME ROOM.
You can see past final exams by going to Old courses page and looking at update pages of past semesters.
PLEASE ALSO STUDY ALL CLASS NOTES, QUIZZES AND TESTS FROM THIS SEMESTER.

ALL OUTSTANDING ISSUES MUST BE CLEARED BY FRI APR 19, 3pm.

GRADES AS OF 4/24 POSTED ON CANVAS, UNDER ANNOUNCEMENTS.

4/24/24 Wednesday
Please read the solutions for the quiz 10.
On friday we will do a review for final.
Quiz 10 solutions

Quiz 10 problems


4/19/24 Friday
QUIZ 10 Wednesday 5.1, 5.2, 5.3, 5.4.
We will work out problems in class on monday.
You will be expected to study notes/ video and come prepared to work on problems in class.
Enough to study practice problems below.

Today talked about eigenvalues, eigenvectors and diagonalization.
Practice problems:
5.1: 1, 5, 9, 13, 21, 22, 31, 32.
5.2: 1, 5, 9, 11, 15.
5.3: 5, 7, 11, 21, 22.
5.4: 5, 13, 18, 19, 20, 21, 22, 23.
Notes for today (read everything starting from "Eigenvalues and eigenvectors") .
Written Notes from class today - part 1 and part 2

TEST 3 APRIL 17 WEDNESDAY.
COVERING ALL MATERIAL AFTER TEST 2. MOR DETAILS SOON.
Upcoming quizzes: 4/12, 4/24.

TEST III WEDNESDAY APR 17.
REVIEW MON APR 15.
Please study 2.8, 2.9, 3.1, 3.2, 3.3, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6.
For chapter 4 enough to read class notes and try practice problems.
Please study all class notes (see below), quiz solutions and practice problems.
Please try Fall 2023 TEST III (all except 3), Please try Spring 2014 TEST III Also try Spring 2011 Test III , and Spring 2009 Test II (except 1, 2), and Spring 2009 Test III (only 1, 2, 4a, 4b)


4/17/24 Wednesday
FRIDAY CLASS WILL BE ON ZOOM. WILL BE IN OFFICE IF YOU NEED ME.

Please read the solutions for the test 3.
We will talk about eigenvalues and eigenvectors on friday.

Test 3 solutions

test 3 problems


4/12/24 Friday
Please read the solutions for the quiz 9.
On Monday we will do a review for test 3.
Quiz 9 solutions

Quiz 9 problems


4/10/24 Wednesday
QUIZ 9 FRIDAY ON 4.3 TO 4.6.
Enough to study practice problems below.

Today talked about coordinates and co-ordinate change in different vector spaces as well as the fact that all bases of the same vector space will have same number of vectors, called the dimension of the space.
Practice problems:
4.3: 3, 5, 9, 11, 15, 21, 29, 31, 33.
4.4: 1, 3, 5, 7, 13, 21.
4.5: 1, 3, 9, 11, 19.
4.6: 1, 5, 9, 17, 18.
Notes for today (read everything upto and before "Eigenvalues and eigenvectors") .

4/8/24 Monday
Today we reviewed vector spaces and subspaces in general, and also talked about basis, dimension and coordinates.
Practice problems:
4.3: 3, 5, 9, 11, 15, 21, 29, 31, 33.
4.4: 1, 3, 5, 7.
Notes for today for 4.3 and 4.4 (Start where it says "Basis and dimension" and read the step 1 "how to find coordinates...") .

4/5/24 Friday
Please read the solutions for the quiz 8.
On Monday we will start 4.3 (basis and dimension).
Quiz 8 solutions

Quiz 8 problems


QUIZ 8 FRIDAY ON 3.3, 4.1, 4.2.

4/3/24 Wednesday
Today we talked about vector spaces and subspaces in general, and showed how column spaces and null spaces are subspaces.
Practice problems:
4.1: 1, 5, 6, 8, 11, 15,21, 23, 24.
4.2: 1, 5, 7, 11, 13, 23, 25, 26.
Notes for today for 4.1 and 4.2 (everything upto where it says "Basis and dimension") .

4/1/24 Monday
Today we talked about Cramer's rule and the adjoint matrix which when divided by the determinant gives the inverse, as well as determinant as volume.
Practice problems:
3.3: 1, 3, 5, 11, 15, 19, 23, 25.
Notes for today for 3.3 (Pearson notes with added slides) .

3/29/24 Friday
Please read the solutions for the quiz 7.
On Monday we will start with 3.3 (inverse's formula).
Quiz 7 solutions

Quiz 7 problems


3/27/24 Wednesday
GRADES AS OF NOW POSTED ON CANVAS.

QUIZ 9 FRIDAY WILL BE ON 7.1 AND 7.2.

3/27/24 Wednesday
GRADES AS OF NOW POSTED ON CANVAS.

QUIZ 7 ON FRIDAY, 2.9 (SEE PROBLEMS BELOW), 3.1, 3.2.

Today we talked about basis and dimension for a bit and then talked about properties of determinants (3.2).
Practice problems:
3.2: 5, 15, 17, 19, 20, 21, 27, 28.
3.1: 1, 3, 7, 9, 33, 35, 36, 37.
2.9: ONLY 15, 17, 18, 19.
Notes for today for 2.9 (Pearson notes with added slides) .
Notes for today for 3.1 (Pearson notes with added slides) .
Notes for today for 3.2 (Pearson notes with added slides) .

3/25/24 Monday
GRADES AS OF NOW POSTED ON CANVAS.

Today we talked about invertible matrix theorem (2.9) and started talking about determinants (3.1).
Practice problems:
3.1: 1, 3, 7, 9, 33, 35, 36, 37.
2.9: 3, 5, 9, 13, 15, 17, 18, 19.
graphic of invertible matrix theorem .
Notes for today for 2.9 (Pearson notes with added slides) .
In above notes please read theorem 15, which we didn't talk about in class, as well.
For example, it says that any two linearly independent vectors are a basis for the 2 dimensional space ( so they automatically span the space).
Also, any two vectors that span the 2-d space will be linearly independent as well.

3/22/24 Friday
GRADES AS OF NOW POSTED ON CANVAS.

Please read the solutions for the quiz 6.
On Monday we will start with 3.1 (determinants).
Quiz 6 solutions

Quiz 6 problems


QUIZ 6 on friday on 2.8 and 2.9. See below for more.

3/20/24 Wednesday
Today we finished talking about subspaces, as well as basis, dimension and coordinates.
Practice problems:
2.8: 1, 3, 5, 7, 15, 17, 21, 22, 23, 25.
2.9: 3, 5, 9, 13, 15, 17, 18, 19.
(Updated-refresh) Notes for today for 2.8 (Pearson notes with added slides) .
Notes for today for 2.9 (Pearson notes with added slides) .

3/18/24 Monday
Today we started talking about subspaces, especially column and null spaces.
Practice problems:
2.8: 1, 3, 5, 7, 10.
Notes for today for 2.8 (Pearson notes with added slides) .

3/15/24 Friday
Please read the solutions for the test 2.
Test 2 solutions

Test 2 problems

On monday we will start 2.8.

TEST II FRIDAY MAR 15.
TEST 2 REVIEW THU MAR 14 ON ZOOM AT 2PM.

For the quiz you can study all of 1.9, 2.1 and 2.2 and 2.3.
For test 2 study 1.6 to 1.9 and 2.1 to 2.3.
Please study all class notes (see below), quiz solutions and practice problems.
Please try Fall 2023 TEST II (all except 2 and 6), Please try Spring 2014 TEST II (all except 4 and 6) Also try Spring 2011 Test II and Spring 2009 Test I (only 6, 7, and 8)


3/13/24 Wednesday
Please read the solutions for the quiz 5.
TEST 2 REVIEW TOMORROW MAR 14 ON ZOOM AT 2PM.
Quiz 5 solutions

Quiz 5 problems


3/11/24 Monday
Today we finished matrix inverses, from 2.2 and 2.3.
Practice problems:
2.2: 1, 5, 8, 9, 25, 31.
2.3: 4, 5, 7, 11, 13, 15, 17, 33, 35, 36, 37.
Notes for today for 2.2 (Pearson notes with added slides) .
Notes for today for 2.3 (Pearson notes with added slides) .


2/28//24 Wednesday
Today we finished linear transformations, from 1.9 and started matrix operations from 2.1.
Practice problems:
1.9: 1, 7, 19, 21, 23, 24, 25, 27, 31, 32, 35, 37, 39.
2.1: 3, 9, 10, 15, 27.
Notes for today for 2.1 (Pearson notes with added slides) .
Notes for today for 1.9 (Pearson notes with added slides) .


2/26/24 Monday
Please read the solutions for the quiz 4.
Quiz 4 solutions

Quiz 4 problems

We will finish 1.9 and start 2.1 on wednesday.

2/23//24 Friday
Today we continued linear transformations, from 1.8 and 1.9.
We will finish the part on one-one and onto. So for the quiz you can study all of 1.8 and 1.9 except for the parts that talk about one-one and onto.
Practice problems:
1.8: 1, 17, 19, 25, 27, 31, 33, 35.
1.9: 1.9: 1, 7, 19, 21, 23, 24. (In 23, 24, ignore the parts involving one-one and onto).
Notes for today for 1.8 (Pearson notes with added slides) .
Notes for today for 1.9 (Pearson notes with added slides) .


2/21//24 Wednesday
Today we talked about linear transformations, from 1.8 and 1.9.
We will finish it on friday.
Please study relevant parts of 1.8 and 1.9:
Practice problems:
1.8: 1, 17, 19, 25, 27, 31, 33, 35.
1.9: 1.9: 1, 7, 19, 21, 23, 24.
Notes for today for 1.8 (Pearson notes with added slides) .
Notes for today for 1.9 (Pearson notes with added slides) .


2/16/24 Friday
Please read the solutions for the quiz 3.
Quiz 3 solutions

Quiz 3 problems

We will start 1.8 on wednesday.

QUIZ 3 FRIDAY FEB 16; TEST II FRIDAY MAR 15.

2/14//24 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.
Notes for today (Pearson notes with added slides)



2/12/24 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.

2/9/24 Friday
Please read the solutions for the test 1.
Test 1 solutions

Test 1 problems

We will start 1.6 on monday.

TEST I NEXT FRIDAY FEB 9 ;
REVIEW FOR TEST 1, ON WEDNESDAY FEB 7 ; STUDY SECTIONS 1.1 TO 1.5.

Please study all class notes (see below), quiz solutions and practice problems.
Please try Fall 2023 TEST I, 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)


2/5/24 Monday
Today we talked about matrix equations, and writing a solution of non-homogenous equation in parametric vector form.
Today's key point was that non-homogenous solutions can be written by translating homogenous solutions by any one non-homogenous solution.
Another point is that homogenous equation has non-trivial solution iff it has free variables, which happens iff there is a non-pivot column in original matrix.
Please try 3, 5, 7, 11, 15, 23, 26 from 1.5.

1/31/24 Wednesday
Today we talked about matrix and vector equations, linear combinations and span, and when a set of vectors spans the whole space.
Today's question was to find the equation of the plane spanned by two vectors in 3 dimensional space. See the notes below for its solution.
Please read these (Updated) Notes on matrix and vector equations.
Please try 25, 26 from 1.3 and 3, 7, 11, 13, 15, 17, 19, 21, 23, 25 from 1.4 in addition to the ones below.

1/29/24 Monday
Please read the solutions for the quiz 2.
Quiz 2 solutions

Quiz 2 problems

We will start 1.4 on wednesday.

1/26/24 Friday
Quiz 2 on monday based on 1.2 (reduced echelon, pivots, free variables) and 1.3 (matrix and vector equations, linear combinations and span).

Today we talked about matrix and vector equations, linear combinations and span.
Please read these Notes on matrix and vector equations.
Please try 1, 3, 5, 7, 9, 11, 13, 23 from 1.3 and 21, 23, 25, and 33 from 1.2. .

1/24/2024 Wednesday
Today we wrapped up 1.2 (reduced echelon, pivots, free variables) and briefly started vector equations (1.3). No new practice problems. Please try 21, 23, 25, and 33 from 1.2 if you haven't already.

1/22/2024 Monday
Please read the solutions for the quiz 1.
Quiz 1 solutions

Quiz 1 problems

We will start 1.3 on wednesday.

1/19/24 Friday
Quiz 1 on monday based on everything we have done in class until wednesday and practice problems given until wednesday.

Today we talked about what how to use row operations to get the reduced echelon matrix from the augmented matrix and to identify the pivot positions.
Please read these Notes on finding Echelon Matrix and pivot positions.
Please try 21, 23, 25, and 33 from 1.2. (These will be for quiz 2, NOT quiz 1 in monday).

1/17/24 Wednesday
Quiz 1 on friday based on everything we have done in class so far and practice problems given below.

Today we talked about what how to use row operations to get the echelon matrixfrom the augmented matrix.
Today's question was: What is the slope of a plane and how do you find it?
Previous questions: Where did we use linear functions in Calculus? How many solutions can a system of 3 linear equations in 3 variables have?
Please read these Notes on basics of Linear Algebra.
In addition to practice problems below, please try 23 and 24 from 1.1 and 1, 3, 7,11,13,15, 17 from 1.2.

1/12/24 Friday
Today we talked about what how to use row operations to solve a system of two equations in two variables.
Please read these Notes on basics of Linear Algebra.
No new practice problems. Have a great weekend!

1/10/24 Wednesday
Today we talked about what Linear Algebra is and why it is important.
Please read these Notes on basics of Linear Algebra.
Please try, as much as you can, the problems 1, 3, 5, 7, 11, 15, 29 from 1.1 (5th edition of Lay's book). We will go over some of them on friday.

1/8/2024 Monday
On wednesday we will continue talking about what Linear Algebra is and why it is important.
We will also start talking about solving systems of linear equations.

Check out this movie Math and movies -- by Numberphile
Fall 2023 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."
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