4 V2 A =|1 4 B = 1 where each x represents an unknown number. Find the Givens rotation matrix G that trans- forms A into B. Report your G and B. [Note: you should do this by hand and show your

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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4
V2
A =|1
4
B =
1
where each x represents an unknown number. Find the Givens rotation matrix G that trans-
forms A into B. Report your G and B. [Note: you should do this by hand and show your
Transcribed Image Text:4 V2 A =|1 4 B = 1 where each x represents an unknown number. Find the Givens rotation matrix G that trans- forms A into B. Report your G and B. [Note: you should do this by hand and show your
Expert Solution
Step 1

Given that,

Advanced Math homework question answer, step 1, image 1

The rotation matrix G is

Advanced Math homework question answer, step 1, image 2

We have to find rotation matrix G which transforms A to B.

Consider the equation

GA = B.

Advanced Math homework question answer, step 1, image 3

By comparing the matrices,

Advanced Math homework question answer, step 1, image 4

Step 2

Solve the equation (1) and (2 simultaneously.

Add equations (1) and (2), 

Advanced Math homework question answer, step 2, image 1

Substitute the value of cos(Θ) in equation (2),

Advanced Math homework question answer, step 2, image 2

 

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