Let u1 = [1, 2, 0], u2 = [-20, 15, 15], u3 = [4, -2, 3] be a basis for R3. Use the Gram-Schmidt process to find an orthogonal basis under the Eculidean inner product.Orthogonal basis: v1 = [1, 2, 0], v2 = [-22, 11, 15], v3 = [a, b, c]Solve for a, b, c. Let2=-20154- {-} -- [E] - []}Աշ15, U33find an orthogonal basis under the Euclidean inner product.be a basis for R³. Use the Gram-Schmidt process to-22°aOrthogonal basis:V1 =V2=V3 =b015a = Ex: 1.23b == Ex: 1.23 €c Ex: 1.230

Let 2 = -20 15 4 - {-} -- [E] - []} Աշ 15 , U3 3 find an orthogonal basis under the Euclidean inner product. be a basis for R³. Use the Gram-Schmidt process to -22° a Orthogonal basis: V1 = V2= V3 = b 0 15 a = Ex: 1.23 b = = Ex: 1.23 € c Ex: 1.230

Let 2 = -20 15 4 - {-} -- [E] - []} Աշ 15 , U3 3 find an orthogonal basis under the Euclidean inner product. be a basis for R³. Use the Gram-Schmidt process to -22° a Orthogonal basis: V1 = V2= V3 = b 0 15 a = Ex: 1.23 b = = Ex: 1.23 € c Ex: 1.230

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 71E

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Question

100%

Let u₁ = [1, 2, 0], u₂ = [-20, 15, 15], u₃= [4, -2, 3] be a basis for R³. Use the Gram-Schmidt process to find an orthogonal basis under the Eculidean inner product.

Orthogonal basis: v₁ = [1, 2, 0], v₂ = [-22, 11, 15], v₃ = [a, b, c]

Solve for a, b, c.

Let
2
=
-20
15
4
- {-} -- [E] - []}
Աշ
15
, U3
3
find an orthogonal basis under the Euclidean inner product.
be a basis for R³. Use the Gram-Schmidt process to
-22°
a
Orthogonal basis:
V1 =
V2=
V3 =
b
0
15
a = Ex: 1.23
b =
= Ex: 1.23 €
c Ex: 1.230

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