### Videos

- Leah Howard's videos for Math 251 can be found here.
- 3Blue1Brown has a nice video series called
Essence of Linear Algebra.
In particular, I recommend:
- Chapter 1: Vectors, what even are they?
- Section 3.5: Linear combinations, span, and basis vectors

### Lecture Notes

- Section 1.1 on Tues., Sept. 4
- Section 1.1, cont'd on Wed., Sept. 5
- We are omitting Binary Vectors and Modular Arithmetic from Section 1.1.
- Section 1.2 on Thurs., Sept. 6
- Section 1.2, cont'd on Fri., Sept. 7
- Section 1.2, cont'd on Mon., Sept. 10
- Section 1.2, cont'd on Tues., Sept. 11
- Cross Product on Tues., Sept. 11
- Cross Product, cont'd on Wed., Sept. 12
- Cross Product, cont'd on Thurs., Sept. 13
- Section 1.3 on Thurs., Sept. 13
- Section 1.3, cont'd on Fri., Sept. 14
- Section 1.3, cont'd on Mon., Sept. 17
- Section 1.3, cont'd on Tues., Sept. 18
- Section 1.3, cont'd on Wed., Sept. 19
- Section 2.1 on Wed., Sept. 19
- Section 2.1, cont'd on Thurs., Sept. 20
- Section 2.2 on Thurs., Sept. 20
- Section 2.2, cont'd on Fri., Sept. 21
- Section 2.2, cont'd on Mon., Sept. 24
- Section 2.2, cont'd on Tues., Sept. 25
- Section 2.3 on Tues., Sept. 25
- Section 2.3, cont'd on Wed., Sept. 26
- Section 2.3, cont'd on Thurs., Sept. 27
- Section 2.3, cont'd on Fri., Sept. 28
- Section 2.4 on Fri., Sept. 28 – there's an error in the RREF for the second problem from the handout that I haven't had time to fix -- sorry about that!
- Section 2.4, cont'd on Mon., Oct 1
- Section 3.1 on Tues., Oct 2
- Section 3.1, cont'd on Wed., Oct 3
- Section 3.2 on Wed., Oct 3
- Test 1 Review on Thurs., Oct 4
- Section 3.2, cont'd on Tues., Oct 9
- Section 3.2, cont'd on Wed., Oct 10
- Section 3.3 on Wed., Oct 10
- Section 3.3, cont'd on Thurs., Oct 11
- Section 3.3, cont'd on Fri., Oct 12
- Section 3.3, cont'd on Mon., Oct 15
- Section 3.4 on Mon., Oct 15
- Section 3.4, cont'd on Tues., Oct 16
- Section 3.5 on Wed., Oct 17
- Section 3.5, cont'd on Thurs., Oct 18
- Section 3.5, cont'd on Fri., Oct 19
- Section 3.5, cont'd on Mon., Oct 22
- Section 3.5, cont'd on Tues., Oct 23
- Section 3.6 on Wed., Oct 24
- Section 3.6, cont'd on Thurs., Oct 25
- Section 3.6, cont'd on Fri., Oct 26
- Complex Numbers on Mon., Oct 29
- Test 2 Review on Tues., Oct 30
- Test 2 Review, cont'd on Wed., Oct 31
- Complex Numbers, cont'd on Wed., Oct 31
- Complex Numbers, cont'd on Thurs., Nov. 1
- Section 4.1 on Tues., Nov. 6
- Section 4.1, cont'd on Wed., Nov. 7
- Section 4.2 on Thurs., Nov. 8
- Section 4.2, cont'd on Fri., Nov. 9
- Section 4.2, cont'd on Tues., Nov. 13
- Section 4.3 on Tues., Nov. 13
- Section 4.3, cont'd on Wed., Nov. 14, with Josh M.
- Section 4.3, cont'd on Thurs., Nov. 15
- Section 4.4 on Thurs., Nov. 15
- No notes for Friday with my substitute, sorry! But you can check last year's archive for that section's notes.
- Section 4.4, cont'd on Mon., Nov. 19
- Section 5.1 on Mon., Nov. 19
- Section 5.1, cont'd on Tues., Nov. 20
- Section 5.1, cont'd on Wed., Nov. 21
- Section 5.2 on Wed., Nov. 21
- Section 5.2, cont'd on Thurs., Nov. 22
- Section 5.3 on Thurs., Nov. 22
- Section 5.3, cont'd on Fri., Nov. 23
- Section 5.4 on Mon., Nov. 26
- Note on Orthogonal Projections on Tues., Nov. 27
- Review for Test 3 on Tues., Nov. 27
- Review for Test 3 on Thurs., Nov. 29
- Section 5.4, cont'd on Thurs., Nov. 29
- Section 7.3 on Mon., Dec. 3
- Section 7.3, cont'd on Tues., Dec. 4
- Section 7.3, cont'd on Wed., Dec. 5
- Review on Wed., Dec. 5
- Review on Thurs., Dec. 6
- Review on Fri., Dec. 7

Lecture notes from Fall, 2017 can be found here. Another good source of notes is Susie Wieler's Lectures page.

### Handouts

- Section 1.1: Properties of Vectors
- Section 1.3: Lines and Planes
- Section 2.2: Homogeneous Systems
- Section 2.4: Applications – there's an error in question 2 that I haven't had time to fix, so please omit!
- Chapter 3: Matrix Properties
- Section 3.5: Change of Basis

### Further Web Resources

The Geogebra simulations shown in class can be found at:

- Section 1.2: Vector projection in 2D
- Cross product
- Section 1.3: Normal to plane
- Section 1.3: Vector equation of a plane
- Section 1.3: Vector equation of a line in 3D
- Section 2.2: Solutions for 3x3 systems
- Section 4.1: Eigenvectors and eigenvalues
- Section 5.3: Gram Schmidt process
- Section 7.3: Least-Squares Approximation

Some students have found the following Wolfram Demonstration useful:

Using Wolfram Alpha to check your calculations:

- Find the dot product of two vectors
- Find the cross product of two vectors
- Project vector A [1,2,3] onto vector B [0,1,0]
- RREF a matrix
- Multiply two matrices
- Find the inverse of a matrix

Try using the Linear Algebra Toolkit to check your calculations. I particularly recommend:

- Row operation calculator
- Calculating the inverse using row operations
- Finding a basis for the null space of a matrix