Question

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.

          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.

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 ℝ^2 about the line that makes
an angle of π/4 (= 45°) with the positive x-axis, and then use that matrix
to find the reflection of (1, 2) onto this line.

Added by Kevin F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Anthony Ramos

06/26/2021

Step 1

Given matrix (b): b = [b1, b2] To find the contraction, we multiply each element by 1/a: contraction = [1/a * b1, 1/a * b2] Show more…

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Texts: (Section 5.4) 4. a. i. Use matrix multiplication to find the contraction of (b) with factor k=1/a, where a>1. 20 points ii. Use matrix multiplication to find the dilation of (b) with factor k=a, where a>1. b. Find the standard matrix for the reflection of IR2 about the line that makes an angle of π/4 (=45°) with the positive x-axis, and then use that matrix to find the reflection of (1,2) onto this line.