(a) Show that {v1, v2, v3} are linearly independent, where[0and v2 =V1 =1and v3 =3Hence {v1, v2, v3} is a basis of V =(b) Find an orthonormal basis of V.span{v1, v2, V3}.

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Answered: (a) Show that {v1, v2, V3} are linearly…

(a) Show that {v1, v2, V3} are linearly independent, where 1 V1 = 1 and v2 = and v3 = -2 Hence {v1, v2, v3} is a basis of V = span{v1, v2, V3}. (b) Find an orthonormal basis of V.

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 41E: Use the inner product u,v=2u1v1+u2v2 in R2 and Gram-Schmidt orthonormalization process to transform...

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Question

(a) Show that {v1, v2, v3} are linearly independent, where
[0
and v2 =
V1 =
1
and v3 =
3
Hence {v1, v2, v3} is a basis of V =
(b) Find an orthonormal basis of V.
span{v1, v2, V3}.

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