#2: 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) vi = (2, 0, , o), v2 = (-rô tô và 0) = ,0), √6 √6 3 2 V3 (B) v2 1 = (-√⁄2, 0, √2, 0), v₂ = (V6, V6, V6, 0), v3 = ( (C) v₁ = (-√2, 0, √2, 0), v₂ = (V6, V6, V6, 0), v3 = (℗D) v₁ = (1, 0, ¹⁄2, 0), v2 = (-√6 V6, V6,0), v3 = ( 3 =(-√3 -√3√3-√3) (√3-√3√3-√3) (√3-√3√3√3) G (EA EA FX- ^^-) = (E) v₁ = (√⁄2, 0, ¹⁄2, 0), v2 = (-V6, -Võ Võ, 0), v3 = (-√³ √³ 13 13 √3 (ⒸF) v₁ = (-√⁄2, 0, √2, 0), v₂ = (√6₁ -√6, V6,0), v3 = (√3₁ √3 √ (G) v₁ = (¹⁄2, 0, ¹⁄2, 0), v₂ = (-V6, -√6 (H) v₁ − (−¹√2, 0, √⁄2, 0), v2 – (V6, -√6 = V6,0), v3 = (-√³ √3 13 13 √√3 √6, 0), v3 = (√3 √3

#2: 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) vi = (2, 0, , o), v2 = (-rô tô và 0) = ,0), √6 √6 3 2 V3 (B) v2 1 = (-√⁄2, 0, √2, 0), v₂ = (V6, V6, V6, 0), v3 = ( (C) v₁ = (-√2, 0, √2, 0), v₂ = (V6, V6, V6, 0), v3 = (℗D) v₁ = (1, 0, ¹⁄2, 0), v2 = (-√6 V6, V6,0), v3 = ( 3 =(-√3 -√3√3-√3) (√3-√3√3-√3) (√3-√3√3√3) G (EA EA FX- ^^-) = (E) v₁ = (√⁄2, 0, ¹⁄2, 0), v2 = (-V6, -Võ Võ, 0), v3 = (-√³ √³ 13 13 √3 (ⒸF) v₁ = (-√⁄2, 0, √2, 0), v₂ = (√6₁ -√6, V6,0), v3 = (√3₁ √3 √ (G) v₁ = (¹⁄2, 0, ¹⁄2, 0), v₂ = (-V6, -√6 (H) v₁ − (−¹√2, 0, √⁄2, 0), v2 – (V6, -√6 = V6,0), v3 = (-√³ √3 13 13 √√3 √6, 0), v3 = (√3 √3

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 41E: Use the inner product u,v=2u1v1+u2v2 in R2 and Gram-Schmidt orthonormalization process to transform...

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