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.

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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.

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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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

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.

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