Day 3: Linear Algebra

Last Time: Linear systems
Announcements:
- Lab 359 hours: 1-2 and 5-10 MWF, 6-10 TR (at least)
- Assignment for next time: Read 1.3; pp. 37-40, problems #4, 5, 8, 10, 11, 14, 18, 22-24, 28, 30, 32
Today:
- Visual review from last time
- Examples from last time:
  - An elementary row reduction program
  - #11, 16, 20, 26
  - 11:
```
0 1 4 -5
1 3 5 -2
3 7 7 6
```
  - 16:
```
1 0 0 -2 -3
0 2 2 0 0
0 0 1 3 1
-2 3 2 1 5
```
- Gaussian elimination: reducing matrices to
  row echelon form:
  1. any rows of zeros are at the bottom
  2. each leading entry of a row is in a column to the right of the leading entry of the row above it
  3. entries below a leading entry are zero
  Reduced row echelon form:
  1. leading entries are 1
  2. eaching leading entry is in a column by itself
  From reduced row echelon form, we can read off the solution set.
- section summary
- Problems:
  - #2, p. 25
  - #7, p. 25 (what's the geometry like?)
    - parameterized solutions
    - basic and free variables
  - #15, p. 25
  - #29, 31, p. 26
Next time: Vector equations

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