please help solve Consider the matrix√ 2 1/2 √ 6 1/2 √√3V6Y011/12 √2√6XGiven that this matrix is orthogonal, determine the unkowns X and Y. Enter each in exact form.What is the answer for X?What is the answer for Y?

Answered: Consider the matrix √2/1/√6 0 1113 V6Y…

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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Question

please help solve

Consider the matrix
√ 2 1/2 √ 6 1/2 √
√3
V6Y
0
11/12 √2
√6
X
Given that this matrix is orthogonal, determine the unkowns X and Y. Enter each in exact form.
What is the answer for X?
What is the answer for Y?

Expert Solution

Step 1: Define the matrix

The given matrix $open square brackets table row cell negative 1 half square root of 2 end cell cell 1 over 6 square root of 6 end cell cell 1 third square root of 3 end cell row 0 cell negative 1 third square root of 6 end cell Y row cell 1 half square root of 2 end cell cell 1 over 6 square root of 6 end cell X end table close square brackets$