See attached image **4.3.1. Determine which of the following matrices are (i) orthogonal; (ii) proper orthogonal.**Given Matrices:1. \[ \begin{pmatrix} \frac{1}{2} & \frac{1}{3} & \frac{1}{4} \\ \frac{1}{3} & \frac{1}{4} & \frac{1}{5} \\ \frac{1}{4} & \frac{1}{5} & \frac{1}{6} \end{pmatrix} \]2. \[ \begin{pmatrix} 0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1 \end{pmatrix} \]3. \[ \begin{pmatrix} -\frac{1}{3} & \frac{2}{3} & \frac{2}{3} \\ \frac{2}{3} & -\frac{1}{3} & \frac{2}{3} \\ \frac{2}{3} & \frac{2}{3} & -\frac{1}{3} \end{pmatrix} \] The task is to determine for each matrix if it is orthogonal or proper orthogonal. An orthogonal matrix has its transpose equal to its inverse, and a proper orthogonal matrix also has a determinant of +1.

Answered: Image /qna-images/answer/8e2999aa-870f-4c58-ba3b-82c0c26de926.jpg

Answered: 4.3.1. Determine which of the following…

4.3.1. Determine which of the following matrices are (i) orthogonal; (ii) proper orthogonal. 01 −1 0 0 0 23 LH STDTE LLL 0 0 -1

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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