I don’t understand here how they got the associated matrix like the part with f(1,0,0,0) and so on are they substituting in the coordinates or in alpha or both ? For a ER consider the linear maps Fa: R² + R² definedas followsfa (x₁y/21t) = (x+2, (2-1) x + 2y + 2, x ²₁ = x + ²y + 32 + t]al Compute the associated matrix to far with respect to the canonical basesR² + REWe are in the dimension of 4 so we have 4 standard basisA=[F(₁) FC₂) F(es) F(14) JF(1,0,0,0) = (-1, α-1, 0,-1)F(0,0,1,0) = (1, 1, α, 3)- 1x-1(²2thway →4+4O 12O1 O2 3A x =L4x1دم()4x4< 1=000C2 =Ps=f(0,1,0,0) = (0, 2, 0, 2)F(0,0,0,1)= (0,0,0,1)

Answered: Image /qna-images/answer/89fe4b7f-fac2-40f1-ac69-8196ff98c502.jpg

Answered: I don’t understand here how they got…

I don’t understand here how they got the associated matrix like the part with f(1,0,0,0) and so on are they substituting in the coordinates or in alpha or both ?

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

I don’t understand here how they got the associated matrix like the part with f(1,0,0,0) and so on are they substituting in the coordinates or in alpha or both ?

For a ER consider the linear maps Fa: R² + R² defined
as follows
fa (x₁y/21t) = (x+2, (2-1) x + 2y + 2, x ²₁ = x + ²y + 32 + t]
al Compute the associated matrix to far with respect to the canonical bases
R² + RE
We are in the dimension of 4 so we have 4 standard basis
A=[F(₁) FC₂) F(es) F(14) J
F(1,0,0,0) = (-1, α-1, 0,-1)
F(0,0,1,0) = (1, 1, α, 3)
- 1
x-1
(²
2thway →
4+4
O 1
2
O
1 O
2 3
A x =
L
4x1
دم
()
4x4
< 1=
000
C2 =
Ps=
f(0,1,0,0) = (0, 2, 0, 2)
F(0,0,0,1)= (0,0,0,1)

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