Let u1 = 1 2 3, u2 = 1 −2 1, u3 = 4 1 −2, and y = 1 −3 11(a) Show that {u1, u2, u3} is an orthogonal basis for R3.(b) Express y as a linear combination of u1, u2, and u3.(c) Normalize u1, u2, and u3 to produce an orthonormal basis {v1, v2, v3} for R3 1Let u₁==U₂ =U3 =1.and y331(a) Show that {u₁, U2, U3} is an orthogonal basis for R³.(b) Express y as a linear combination of u₁, u2, and u3.(c) Normalize u₁, u2, and u3 to produce an orthonormal basis {V₁, V2, V3} for R³.

Answered: Image /qna-images/answer/3150f834-be2d-4c37-8b13-52738113b352.jpg

1 Let u₁= = U₂ = U3 = 1. and y 3 3 1 (a) Show that {u₁, U2, U3} is an orthogonal basis for R³. (b) Express y as a linear combination of u₁, u2, and u3. (c) Normalize u₁, u2, and u3 to produce an orthonormal basis {V₁, V2, V3} for R³.

1 Let u₁= = U₂ = U3 = 1. and y 3 3 1 (a) Show that {u₁, U2, U3} is an orthogonal basis for R³. (b) Express y as a linear combination of u₁, u2, and u3. (c) Normalize u₁, u2, and u3 to produce an orthonormal basis {V₁, V2, V3} for R³.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 16CM

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Question

Let u1 = 1 2 3, u2 = 1 −2 1, u3 = 4 1 −2, and y = 1 −3 11
(a) Show that {u1, u2, u3} is an orthogonal basis for R3.
(b) Express y as a linear combination of u1, u2, and u3.
(c) Normalize u1, u2, and u3 to produce an orthonormal basis {v1, v2, v3} for R3