1. 2.1 Day 3 Linear Transformations

2. Library of basic matrices
What matrices do we have in our library of basic matrices?

3. 32 Solution
Use your knowledge of matrix multiplication to justify why this
matrix results in a scaling.
What is the general form of a matrix that scales inputs by a factor of b.

4. Problem 33

5. 33 Solution

6. Note the procedure for problem 33 in n dimensions

7. Problem 34

8. 34 Solution
Please record this for use in future sections (see next slide)

9. Rotations
The matrix of counterclockwise rotation in real 2 dimensional space through angle theta is
Note this is a matrix of the form

10. Problem 13b prove this formula

11. Homework p all, 39,40,41,42 Use elementary matrices to create a matrix that will rotate points clockwise
Note: Record your answers to 24 – 30 for future use as examples of transformation matrices

12. Proof of Cramer’s rule

13. The idea from problem 13 expands into 3x3
(explained on the next slide)

14. Explanation of adjoint and inverse rule