### 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

### My Current Lecture Notes

- Section 1.1
- We are omitting Binary Vectors and Modular Arithmetic from Section 1.1.
- Section 1.2
- Cross Product
- Section 1.3
- Section 2.1
- Section 2.2
- Section 2.3
- Section 2.4
- Section 3.1
- Section 3.2
- Section 3.3
- Section 3.4
- Section 3.5
- Section 3.6
- Complex Numbers
- Section 4.1
- Section 4.2
- Section 4.3
- Section 4.4
- Section 5.1
- Section 5.2
- Section 5.3
- Section 5.4

Lecture notes from Fall, 2018 can be found here. I also used these for the fully online section of Math 251 in Fall 2020.

### Test Review

Test review from Fall, 2018 (and Fall 2020) can be found in amongst the old lecture notes here.

### 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: Gauss-Jordan Method

For RREF calculations, I particularly recommend Adrian Stoll's RREF Calculator. This one's particularly great because your matrix can include complex numbers.

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