Let R have the Euclidean inner product, and let W be the subspace spanned by the vectors u₁ = (-1, 0, 1, 0), u2 = (0, -1, 1, 0), and u3 = (0, 0, 1,-1). Use the Gram-Schmidt process to transform the basis {u₁, u2, u3} into an orthonormal basis. (A) v₁ = (-√2, 0, 2,0), v2 = (№6 V6 V6, 0), v3 =(√3, 3 33 (B) v₁ = (√2,0, ¹2, 0), v2 -(-V6 V6 V6,0), v3 = (-√3 13 13 13 = 3 (C) v₁ = (-√2,0,2,0), v2 = (V6, -V6 V6,0), v3 = (√3 13 13 13 (D) v₁ - (√2,0, 2,0), v₂ -(-V6, V6 V6 0), v3 - (-√3131313 = = V2 (E) v₁ - (2.0.2.0). v2 -(-V6, -6, V6,0). v3 -(-VVV-V (-13 13 √6 = = (v₁- (2.0.2.0). v2-(-Vo vo V6.0). v3 - (-) (F) = 0, √6 = 3 V3 = (G) v₁ - (-√2, 0, √2,0), v₂ - (V6, -V6, V6,0), v3 - (√3 √ = V2 (H) v₁ = (-√2,0, √2, 0), v₂ = (V6 V6 V6,0), v3 =(√3, 333 V2

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 R4 have the Euclidean inner-product, and let W be the subspace spanned by the vectors
u₁ = (1, 0, 1, 0), u₂
(0, -1, 1, 0), and u3 = (0, 0, 1, -1).
Use the Gram-Schmidt process to transform the basis {u₁, u2, u3} into an orthonormal basis.
√6
(4) v₁ = (-1⁄2, 0, √2, 0), v2 = (V6 V6 V6, 0), v3 - (√3-√3 √√3
=
3
6
6 6
(B) v₁ = (√2,0, 2,0), v2 = (-V6, V6 V6, 0), v3 = (-√3-√3√3√3)
6
Problem #2:
=
(C)V₁-(-2,0,2,0). ₂ - (V6, -V6, V6.0). v3 - (
V2 =
(D) v₁ = (√2,0, 2,0), v₂ = (-V6, -V6, V6,0). v3 - (-√3 13 13 13
V2
=
6
(E) v₁ = (√2,0, ¹2,0), v₂ = (-V6, -V6 V6,0), v3 = (-√3, V3 √3
6
(F) v₁-(2,0.2.0). v2-(-V6 V6 V6,0), v3 - (-)
=
=
(G) v₁ - (-2.0.2.0). v₂ - (Vo. Vo V6 0). v3 - (
=
V3
Select
6 6 6
(H) v₁ - (-2,0,2,0). v₂ - (V6 V6, V6,0). v3 - (VVV-VI)
=
V2
V3
Transcribed Image Text:Problem #2: Let R4 have the Euclidean inner-product, and let W be the subspace spanned by the vectors u₁ = (1, 0, 1, 0), u₂ (0, -1, 1, 0), and u3 = (0, 0, 1, -1). Use the Gram-Schmidt process to transform the basis {u₁, u2, u3} into an orthonormal basis. √6 (4) v₁ = (-1⁄2, 0, √2, 0), v2 = (V6 V6 V6, 0), v3 - (√3-√3 √√3 = 3 6 6 6 (B) v₁ = (√2,0, 2,0), v2 = (-V6, V6 V6, 0), v3 = (-√3-√3√3√3) 6 Problem #2: = (C)V₁-(-2,0,2,0). ₂ - (V6, -V6, V6.0). v3 - ( V2 = (D) v₁ = (√2,0, 2,0), v₂ = (-V6, -V6, V6,0). v3 - (-√3 13 13 13 V2 = 6 (E) v₁ = (√2,0, ¹2,0), v₂ = (-V6, -V6 V6,0), v3 = (-√3, V3 √3 6 (F) v₁-(2,0.2.0). v2-(-V6 V6 V6,0), v3 - (-) = = (G) v₁ - (-2.0.2.0). v₂ - (Vo. Vo V6 0). v3 - ( = V3 Select 6 6 6 (H) v₁ - (-2,0,2,0). v₂ - (V6 V6, V6,0). v3 - (VVV-VI) = V2 V3
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