Problem #5: Let W be the subspace of R4 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 = (-V6, -√6₁ √6,0), v3 = (B) V₁ = =(√2,0,2,0), v₂ = ), v2 = (-√6 √6 √6,0), v3 = (C) v₁ = (-√₂, 0, √₂,0), v₂ = (√6 (√6 V6 √6,0), v3 = 3 (D) v₁ = (√2,0,2,0), v₂ = -(-V6 V6 √6,0), V3 = 3 (E) V₁ = = (-2,0,2,0), v2 = (F) V₁ = (G) v₁ = (-√3 √3 √3 (-√3-√3 √/30 (√3, -√3 √3, -√3) (V6 (H) V₁ = (-√2,0,2,0), v₂ = =(-1/3-√3√3+√3) 6 6 (√3, 1/2 = (-√2,0,√2,0), v₂ = (√6₁ -√6, V6,0), v3 = (√³ √3 √3₁ √6 √6,0), V3 = 6 =(√2,0,2,0), v2 = (-√6. -√6 √6,0), v3 = 3 (√3-√√√3) 6 V2 (V6, -√6 V6,0), v3 = (-√3 √3 √3-√3) >
Problem #5: Let W be the subspace of R4 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 = (-V6, -√6₁ √6,0), v3 = (B) V₁ = =(√2,0,2,0), v₂ = ), v2 = (-√6 √6 √6,0), v3 = (C) v₁ = (-√₂, 0, √₂,0), v₂ = (√6 (√6 V6 √6,0), v3 = 3 (D) v₁ = (√2,0,2,0), v₂ = -(-V6 V6 √6,0), V3 = 3 (E) V₁ = = (-2,0,2,0), v2 = (F) V₁ = (G) v₁ = (-√3 √3 √3 (-√3-√3 √/30 (√3, -√3 √3, -√3) (V6 (H) V₁ = (-√2,0,2,0), v₂ = =(-1/3-√3√3+√3) 6 6 (√3, 1/2 = (-√2,0,√2,0), v₂ = (√6₁ -√6, V6,0), v3 = (√³ √3 √3₁ √6 √6,0), V3 = 6 =(√2,0,2,0), v2 = (-√6. -√6 √6,0), v3 = 3 (√3-√√√3) 6 V2 (V6, -√6 V6,0), v3 = (-√3 √3 √3-√3) >
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem #5: Let W be the subspace of Rª spanned by the vectors
(-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.
一点点点
ui =
协) (0) = (07)
6
(A) V1 =
(B) vi = (2,0,0,0), v2 =
V1
V2
(600,0), vs =
(C)V1 = (550,0,0), 2 = (6600), vs =
V2
(D)V1 = (2,0,0,0), 2 = (6,500), vs =
v1
V2
v3
6'3"
{EW} = (2,0,0,0), 12 = (66)
(一兵,0,0,0).
(E) V1
V2
3
(F) V1 =
(G) v = (2,0,0,0), V2 =
,0),
V2
V3
(一点一点点
(嘻嘻嘻)
(嘻嘻嘻)
= (5)
(嘻嘻)
6
2
= && (0*) = &ozoz)
(嘻嘻嘻)
6 6
(66676)
,0), v3 =
(H) v = (-¹.0, ¹.0), v2=(√√√.0), 3(√√√
V1
哈
2
V3 =
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6
2
6
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