2.1 Day 3 Linear Transformations

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

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.

Problem 33

33 Solution

Note the procedure for problem 33 in n dimensions

Problem 34

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

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

Problem 13b prove this formula

Homework p. 51 24 - 32all, 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

Proof of Cramer’s rule http://en.wikipedia.org/wiki/Cramer%27s_rule

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

Explanation of adjoint and inverse rule