linear algebraVerify thatu1,u2is an orthogonal set, and then find the orthogonal projection of y ontoSpanu1,u2. y=45−5,u1=320,u2=−230 Question content area bottomPart 1To verify thatu1,u2is an orthogonal set, findu1•u2. u1•u2=Start 3 By 1 Table 1st Row 1st Column 4 2nd Row 1st Column 5 3rd Row 1st Column 0 EndTable 4 50(Simplify your answer.) Verify that {₁,2} is an orthogonal set, and then find the orthogonal projection of y onto Span {₁,₂}.y =5, U₁ =-5U₁ • U₂3LO0, 4₂:- 2To verify that {₁,₂} is an orthogonal set, find u₁ • U₂.4-800(Simplify your answer.)Try again.U₁424and v=unIf u and v are vectors in Rn, with u =u•V=U₁V₁+U2V₂ ++ Un V'nᵒn':OK√₁V2Vnthen u v=u'v, or=uTv, orX

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Answered: Verify that (u₁,u₂} is an orthogonal…

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 content area bottom

Part 1

To verify that

u1,u2

is an orthogonal set, find

u1•u2.

u1•u2=Start 3 By 1 Table 1st Row 1st Column 4 2nd Row 1st Column 5 3rd Row 1st Column 0 EndTable

	4
5
0

(Simplify your answer.)

Verify that {₁,2} is an orthogonal set, and then find the orthogonal projection of y onto Span {₁,₂}.
y =
5, U₁ =
-5
U₁ • U₂
3
LO
0
, 4₂:
- 2
To verify that {₁,₂} is an orthogonal set, find u₁ • U₂.
4
-8
0
0
(Simplify your answer.)
Try again.
U₁
42
4
and v=
un
If u and v are vectors in Rn, with u =
u•V=U₁V₁+U2V₂ ++ Un V
'nᵒn'
:
OK
√₁
V2
Vn
then u v=u'v, or
=uTv, or
X

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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