Let R have the Euclidean inner product, and let W be the subspace spanned by the vectors up = (-1,0,1,0), u2 = (0,-1,1,0), and u3 = (0,0,1,1). Use the Gram-Schmidt process to transform the basis {uy, u2, u3} into an orthonormal basis. (A) = (2,04,0), 2 = (D) = (D) (B) V1 = (2,0,0,0). 2 = (DDD) (D) V2 (6) 嘻嘻嘻) On = (2,000) 2 = V = ()() = (07) = (a) (E) V1 = OF V = (2,050) 2 (66) V2 (G) v = (0) 2 = (6) DV-50502 (6) 3 1=(√2.0.2.0). v₂ = (√ √ √6.0), v3=(√√√√ = E VB = =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem #2: Let R' have the Euclidean inner product, and let W be the subspace spanned by the vectors
up = (-1,0,1,0), u2 = (0,-1,1,0), and us = (0,0,1,1).
Use the Gram-Schmidt process to transform the basis {uy, uz, us} into an orthonormal basis.
(A) = (1050) 2 = (DDD)
(D)
(B) vi = (2,0,0,0), v2 = (66) (0)
V2
1 = (0) 2 = 6,56)
(66)
(0)
(D)V1 = (2000) 2 = (66)
1 = (0) 2 = (66)
V2
(F) V1 =
=
1 = 0.00) 2 (6)
(G) vi = (2,05,0), 12 ( 666)
VI =
3
V =
3
=
=
V =
=
CHIV = (0.00) 2 ()()
V2 =
Transcribed Image Text:Problem #2: Let R' have the Euclidean inner product, and let W be the subspace spanned by the vectors up = (-1,0,1,0), u2 = (0,-1,1,0), and us = (0,0,1,1). Use the Gram-Schmidt process to transform the basis {uy, uz, us} into an orthonormal basis. (A) = (1050) 2 = (DDD) (D) (B) vi = (2,0,0,0), v2 = (66) (0) V2 1 = (0) 2 = 6,56) (66) (0) (D)V1 = (2000) 2 = (66) 1 = (0) 2 = (66) V2 (F) V1 = = 1 = 0.00) 2 (6) (G) vi = (2,05,0), 12 ( 666) VI = 3 V = 3 = = V = = CHIV = (0.00) 2 ()() V2 =
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