1. Show that the vectors (1/(3√2), 1/(3√√2), –4/(3√√2))¹, (2/3,2/3,1/3), (1/√√2, -1/√√2,0)¹ form an orthonormal basis of R³. Find the coordinates of the vector (1, 4, 3) with respect to that basis.
1. Show that the vectors (1/(3√2), 1/(3√√2), –4/(3√√2))¹, (2/3,2/3,1/3), (1/√√2, -1/√√2,0)¹ form an orthonormal basis of R³. Find the coordinates of the vector (1, 4, 3) with respect to that basis.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.3: Orthonormal Bases:gram-schmidt Process
Problem 71E
Related questions
Question
![1. Show that the vectors
(1/(3√2), 1/(3√√2), -4/(3√√/2)), (2/3,2/3, 1/3), (1/√√2, -1/√√2,0)
form an orthonormal basis of R³. Find the coordinates of the vector
(1, 4, 3) with respect to that basis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda22bb93-89e0-43b0-b495-0a6067b20da3%2Fe62239e1-dd28-4ec7-9a69-ab9bf17b313d%2F8da1ssw_processed.png&w=3840&q=75)
Transcribed Image Text:1. Show that the vectors
(1/(3√2), 1/(3√√2), -4/(3√√/2)), (2/3,2/3, 1/3), (1/√√2, -1/√√2,0)
form an orthonormal basis of R³. Find the coordinates of the vector
(1, 4, 3) with respect to that basis.
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