CHALLENGEACTIVITY7.4.1: Finding an orthogonal basis using the Gram-Schmidt process.469360.2546800.qx3zqy7Jump to level 120Let {U₁ = [ ²₁ 2], 0r = [-2₁ -18].[3]}U₂, U3=-18Use the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product.a{K₁ = [₁₂2] · M = [81] ₂ B =,-1-4Orthogonal basis:a = Ex: 5b = Ex: 5C = Ex: 1.23be a basis for a subspace of R2x2-1.59-1.65d = Ex: 1.23с3}

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Jump to level 1 Let (U₁=[2₁2] ₂-[-1818)-[3]} U3 = 0 Use the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product. Orthogonal basis: V₁ a = Ex: 5 b: 0 0 a 1.59 * {v₁ = [²₁₂2] ·M = [8 -¹8]. ³₁ = [1185 2]} V₂ V3 -1 -1.65 Ex: 5 0 C = Ex: 1.23 be a basis for a subspace of R2x2. d=Ex: 1.23

Jump to level 1 Let (U₁=[2₁2] ₂-[-1818)-[3]} U3 = 0 Use the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product. Orthogonal basis: V₁ a = Ex: 5 b: 0 0 a 1.59 * {v₁ = [²₁₂2] ·M = [8 -¹8]. ³₁ = [1185 2]} V₂ V3 -1 -1.65 Ex: 5 0 C = Ex: 1.23 be a basis for a subspace of R2x2. d=Ex: 1.23

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

CHALLENGE
ACTIVITY
7.4.1: Finding an orthogonal basis using the Gram-Schmidt process.
469360.2546800.qx3zqy7
Jump to level 1
2
0
Let {U₁ = [ ²₁ 2], 0r = [-2₁ -18].[3]}
U₂
, U3
=
-18
Use the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product.
a
{K₁ = [₁₂2] · M = [81] ₂ B =
,
-1
-4
Orthogonal basis:
a = Ex: 5
b = Ex: 5
C = Ex: 1.23
be a basis for a subspace of R2x2-
1.59
-1.65
d = Ex: 1.23
с
3}

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469360.2546800.qx3zqy7
Jump to level 1
20
0
-2
3
Let
{ " = [ 2² ] ₁0 - [18] - [1 2]}
=
U₁
,U₂
, U3
-2
16
0
the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product.
Orthogonal basis: V₁
a = Ex: 5
a
= {v₁ -[-²8] ·½ - [8 8]·²-[-0.67 2]}
= |
V₂ =
=
b=
||
Ex: 5
C = Ex: 1.23
d=
be a basis for a subspace of R2x2. Use
=
Ex: 1.23
2
3
5

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