QUESTION 10 Let's try to the Gram-Schmidt process of orthogonalization with the matrix 0.223 0.668 0.710 -0.125 0.741 0.660 0.795 -0.234 0.560 What is the x-coordinate of r3-prime? (don't normalize r3-prime, simply follow the steps, do not use the cross product) Round your answer to 3 decimal places.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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QUESTION 10
Let's try to the Gram-Schmidt process of orthogonalization with the matrix
0.223 0.668 0.710
-0.125 0.741 0.660
0.795 -0.234 0.560
What is the x-coordinate of r3-prime? (don't normalize r3-prime, simply follow the steps, do not use the cross product)
Round your answer to 3 decimal places.
Transcribed Image Text:QUESTION 10 Let's try to the Gram-Schmidt process of orthogonalization with the matrix 0.223 0.668 0.710 -0.125 0.741 0.660 0.795 -0.234 0.560 What is the x-coordinate of r3-prime? (don't normalize r3-prime, simply follow the steps, do not use the cross product) Round your answer to 3 decimal places.
Expert Solution
Step 1

Given matrix 0.2230.6680.710-0.1250.7410.6600.795-0.2340.560

Let 

r1=0.223, 0.668, 0.710r2=-0.125, 0.741, 0.660r3=0.795, -0.234, 0.560

Use gram schmidt process of orthogonalization.

r1'=r1=0.223, 0.668, 0.710

r2'=r2-r1'·r2r1'·r1'r1'

r1'·r1'=0.223, 0.668, 0.710·0.223, 0.668, 0.710           =0.2232+0.6682+0.7102           =1.0001

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