(1) Let ---1-0 uj = |3 u2 = uz = Apply the Gram-Schmidt process to u1, u2, uz in this order. The resulting vectors are v1 = V2 = ,v3 = and B = {v1, v2, v3} is an orthogonal basis for R³. (ii) Express the vector as a linear combination of v1, v2 and vz: 1 v1+ v2+ v3 )

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) Let
u1 = |3
u2
uz =
3
Apply the Gram-Schmidt process to u1, u2, uz in this order. The resulting vectors are
v1 =
v2 =
v3 =
and B = {v1, v2, v3} is an orthogonal basis for R°.
(ii) Express the vector
1
as a linear combination of v1, v2 and vz:
1
=
vi+
v2+
v3 )
Transcribed Image Text:(1) Let u1 = |3 u2 uz = 3 Apply the Gram-Schmidt process to u1, u2, uz in this order. The resulting vectors are v1 = v2 = v3 = and B = {v1, v2, v3} is an orthogonal basis for R°. (ii) Express the vector 1 as a linear combination of v1, v2 and vz: 1 = vi+ v2+ v3 )
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