Q8. Consider i, w E R² as below, where w is the reflection of across the x-axis. (Note: These vectors have nonzero x- and Y-components, i.e., they are not on the axes.) y W (a) If Av = w and Aw = v, show that A is reflection across the x- axis, i.e., A (b) If Að = w and Aw = -6, show that A is similar to a rotation matrix.
Q8. Consider i, w E R² as below, where w is the reflection of across the x-axis. (Note: These vectors have nonzero x- and Y-components, i.e., they are not on the axes.) y W (a) If Av = w and Aw = v, show that A is reflection across the x- axis, i.e., A (b) If Að = w and Aw = -6, show that A is similar to a rotation matrix.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 32E
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part a
Given that be two vectors in such that is the reflection of across axis.
Let us consider
Now, suppose , where and are constants to be determined. It is given and
Similarly, from , we have
Hence, is given by
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