Day 3: Linear Algebra

Last Time: Linear systems
Announcements:
- Lab 359 open hours are posted on the door; I'm in the process of getting you all accounts (if you don't already have one) .
Today:
- Quick Examples from section 1.1:
  - p. 11, #12, 15, 20, 26, 32
  - Solutions for
- An elementary row reduction program
  For example, #12:
```
 1 -3  4 -4
 3 -7  7 -8
-4  6 -1  7
```
  Augmented matrix for #15:
```
1   0   3   0   2
0   1   0  -3   3
0  -2   3   2   1
3   0   0   7  -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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