20 points
4.
(Section 5.4)
a. i. Use matrix multiplication to find the contraction of (a, b) with factor
k = 1/a, where a > 1.
ii. Use matrix multiplication to find the dilation of (a, b) with factor
k = a, where a > 1.
b. Find the standard matrix for the reflection of \(\mathbb{R}^2\) about the line that makes
an angle of \(\pi/4\) (= 45°) with the positive x-axis, and then use that matrix
to find the reflection of (1, 2) onto this line.