assigned today:

Due today:

- standard-linear vector spaces:
I can determine the rank of a matrix and whether vectors are linearly independent.

- Prove that any 3 non-zero 2d vectors are linearly dependent.
- Prove that the determinant of a system equations (not all of which equal zero) that has multiple solutions is zero.
- 7.7.20 (a) and (b).

Due today:

- standard-matrices and gaussian elimination:
I can manipulate matrices and solve systems of linear equations.

- 7.2.28
- Explain figure 158
- 7.3.17

- linear independence and spanning the space
- reinterpretation of the matrix equation
- determinant
- specifically an all zero row

- matrix inversion

- quiz on Markov
- we talked a lot about it afterwards

- 3 vectors in 2d that come back to origin
- had to say that they needed to have a net non-zero contribution

- 2 vectors to get to a random point in 2d
- discussed similarities between those two approaches

- talked about homogeneous (too many solutions)
- talked about determinant and how it helps find if it's homogeneous
- kind of ran out of time to pull it all together