# Mathematical and Computational Methods in Physics and Engineering (fall 2016)

## Daily outline for Wed, Sep 21, 2016 9:10 AM (1 year ago)

### Linear Algebra 1

assigned today:
• standard-matrices and gaussian elimination:

I can manipulate matrices and solve systems of linear equations.

1. 7.2.28
2. Explain figure 158
3. 7.3.17

Due today:

# Plan

• What are linear transformations?
• graphics
• operations
• add, scalar multiply, matrix multiply
• If you know the transformation and one result, how do you find the original?
• Gaussian elimination

# What we did

• Quiz on $$\sin5\theta$$
• they asked for Pascal's triangle so I kept writing until they told me to stop so that I wasn't immediately clear which row to use
• Asked them to write the formula for a transformation that takes an ordered pair and returns an ordered pair
• very similar to complex mapping we did a week ago
• Talked about the limitation to linear transformations (x and y to the first power only and no constants)
• talked about how a matrix is shorthand for the transformation
• Asked what a grid of points would do after a transformation
• then did it in MMA along with watching a random shape
• asked if the shape every inverted or if it just rotated (along with being smushed).
• Talked about multiplying by a scalar, adding two transformations, and multiplying two transformations
• Asked them to do 2 2x2 transforms in a row to prove matrix multiplication
• many just did matrix multiplication :)
• quickly discussed Gaussian elimination

edit