Let V = span{v1 = (1, 1, 2), v2 = (0, 1, 1), v3 = (-1, 0, -1)} be the subspace of R^3 endowed with the usual inner product. A) Find an orthonormal basis of V. B) Find an orthonormal basis of the orthogonal complement VI of V. C) Compute the orthogonal projections of the vector v = (−2, −1, 1) onto V and VI.
Let V = span{v1 = (1, 1, 2), v2 = (0, 1, 1), v3 = (-1, 0, -1)} be the subspace of R^3 endowed with the usual inner product. A) Find an orthonormal basis of V. B) Find an orthonormal basis of the orthogonal complement VI of V. C) Compute the orthogonal projections of the vector v = (−2, −1, 1) onto V and VI.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 41CR: Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the...
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Transcribed Image Text:Let V = span{v1 = (1, 1, 2), v2 = (0, 1, 1), v3
= (-1, 0, -1)} be the subspace of R^3
endowed with the usual inner product.
A) Find an orthonormal basis of V.
B) Find an orthonormal basis of the
orthogonal complement VI of V.
C) Compute the orthogonal projections
of the vector v = (−2, −1, 1) onto V and
VI.
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