Given v = U1 = -3 2 find the coordinates for v in the subspace W spanned by -1 1 -1 1 0 -2 [] B 1 1 Note that u₁, 2 and u3 are orthogonal. Ou₁+ V= -9 I U2 = U₁+U₂+uz and uz = 1

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 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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Given v =
U1 =
-3
2
find the coordinates for v in the subspace W spanned by
-1
1
-1
1
0
-2
[]
D
1
1
Note that u₁, 2 and u3 are orthogonal.
=0u₁+
V=
-9
I
U2 =
u2+ Uz
and uz
=
1
Transcribed Image Text:Given v = U1 = -3 2 find the coordinates for v in the subspace W spanned by -1 1 -1 1 0 -2 [] D 1 1 Note that u₁, 2 and u3 are orthogonal. =0u₁+ V= -9 I U2 = u2+ Uz and uz = 1
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