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
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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.
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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