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Consider the Euclidean inner product space with a basis B = {(1, 1, 1), (0, 1, 1), (0,0,1)}. Find an orthogonal basis of R³.

Consider the Euclidean inner product space with a basis B = {(1, 1, 1), (0, 1, 1), (0,0,1)}. Find an orthogonal basis of R³.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 40EQ
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Consider the Euclidean inner product space R³ with a basis B = {(1, 1, 1), (0, 1, 1), (0,0,1)}. Find an orthogonal basis of R³. A. {(1, -2, 1), (0, – 1, − 1), (0,1,0) } B. {(2,1,1), (0, 1, 1), (0, – 1,1) } C. {(1,1,1),(-2,1,1),(0, – 1,1) } ○ D. {(1,1,1),(0,0,1), (0, – 1,1) } O E. None in the given list.
Transcribed Image Text:Consider the Euclidean inner product space R³ with a basis B = {(1, 1, 1), (0, 1, 1), (0,0,1)}. Find an orthogonal basis of R³. A. {(1, -2, 1), (0, – 1, − 1), (0,1,0) } B. {(2,1,1), (0, 1, 1), (0, – 1,1) } C. {(1,1,1),(-2,1,1),(0, – 1,1) } ○ D. {(1,1,1),(0,0,1), (0, – 1,1) } O E. None in the given list.
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