1. Consider the polynomials for k = 0,1, ..,11, and let B = {bo,b1,., bị1}. It can be shown that B is a basis for P11, the vector space of polynomials of degree at most 11. (You do not need to prove this.) Let pr (x) = x* for k = 0, 1,., 11, so that S = {po,P1,...,P11} is the standard basis for P11. Use Mathematica to: Monas onash ash ask (a) Compute the change of basis matrix PB→s. task (b) Uni sable ta essae task (c) Find task Copyn pyr Compute the change of basis matrix PsR. Gers br (x) := (1 – x)*g11-k the coordinate vector of the polynomial Assessable Ass Monash Monash Univ with a respect to the basis B. cht Monash Univer Hint: You may find the Mathematica command CoefficientList [p(x),x] useful. For a given polynomial p(x) = co +c1x + c2x² + · .+ Cnx" in x, CoefficientList [p(x),x] returns the list of coefficients {co,c1, ..,Cn}. task op sessa Ssessa Gessab sable able University able t le tash Copy ht Monash Universi Copye Copyrige Monash U 2021 nash niv ight Moneh U Monas iv 2710 2021 sh Universi University ersity ple t Ssessabl sable Asse pyright yright Monash onash Univer versity 202 ersity 2021.
1. Consider the polynomials for k = 0,1, ..,11, and let B = {bo,b1,., bị1}. It can be shown that B is a basis for P11, the vector space of polynomials of degree at most 11. (You do not need to prove this.) Let pr (x) = x* for k = 0, 1,., 11, so that S = {po,P1,...,P11} is the standard basis for P11. Use Mathematica to: Monas onash ash ask (a) Compute the change of basis matrix PB→s. task (b) Uni sable ta essae task (c) Find task Copyn pyr Compute the change of basis matrix PsR. Gers br (x) := (1 – x)*g11-k the coordinate vector of the polynomial Assessable Ass Monash Monash Univ with a respect to the basis B. cht Monash Univer Hint: You may find the Mathematica command CoefficientList [p(x),x] useful. For a given polynomial p(x) = co +c1x + c2x² + · .+ Cnx" in x, CoefficientList [p(x),x] returns the list of coefficients {co,c1, ..,Cn}. task op sessa Ssessa Gessab sable able University able t le tash Copy ht Monash Universi Copye Copyrige Monash U 2021 nash niv ight Moneh U Monas iv 2710 2021 sh Universi University ersity ple t Ssessabl sable Asse pyright yright Monash onash Univer versity 202 ersity 2021.
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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Need help with part b). Please Mathematica and show commands used. Thank you :)
![1. Consider the polynomials
for k = 0,1, ...,11, and let B = {bo,b1,., b11}. It can be shown that B is a basis for P1, the vector space of polynomials of degree
at most 11. (You do not need to prove this.) Let pr(x) = xk for k = 0,1, ..., 11, so that S = {p0, P1,...,Pu} is the standard basis for
P11. Use Mathematica to:
ona
Monash
(a) Compute the change of basis matrix PB→s.
task
le task,
able task.
Univ
nivers
(b) Compute the change of basis matrix Ps-R.
ssable ta
e tas
Copyi
opvrigi
| the coordinate vector of the polynomial
nas
Monash
Monash
ASsessabl ask,
Assessable
sesse
ble tas
task,
with
respect to the basis B.
opy
yrigl
2021.
2021. A
Asse
Hint: You may find the Mathematica command CoefficientList [p(x),x] useful. For a given polynomial
sessa
essable
ht Monash Universi
q(x) = x + 2x³ – 2x4 + x²
Assess
Ssessal
p(x) = co + c1x + c2x² + · . - + Cnx" in x, CoefficientList[p(x),x] returns the list of coefficients {co, c1,. .., Cn}.
le task,
sk. Copy
sity
2021
2021.
esable
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ash UniversH
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essable
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Transcribed Image Text:1. Consider the polynomials
for k = 0,1, ...,11, and let B = {bo,b1,., b11}. It can be shown that B is a basis for P1, the vector space of polynomials of degree
at most 11. (You do not need to prove this.) Let pr(x) = xk for k = 0,1, ..., 11, so that S = {p0, P1,...,Pu} is the standard basis for
P11. Use Mathematica to:
ona
Monash
(a) Compute the change of basis matrix PB→s.
task
le task,
able task.
Univ
nivers
(b) Compute the change of basis matrix Ps-R.
ssable ta
e tas
Copyi
opvrigi
| the coordinate vector of the polynomial
nas
Monash
Monash
ASsessabl ask,
Assessable
sesse
ble tas
task,
with
respect to the basis B.
opy
yrigl
2021.
2021. A
Asse
Hint: You may find the Mathematica command CoefficientList [p(x),x] useful. For a given polynomial
sessa
essable
ht Monash Universi
q(x) = x + 2x³ – 2x4 + x²
Assess
Ssessal
p(x) = co + c1x + c2x² + · . - + Cnx" in x, CoefficientList[p(x),x] returns the list of coefficients {co, c1,. .., Cn}.
le task,
sk. Copy
sity
2021
2021.
esable
ble tas
| Monash U
Copyrig
Copyright
yright Mogash
Monasi
ight Moneh Un
20
Monash Univer
ash UniversH
University
Iniversity
onash
dash Un
ights
able ta
htMonash Uni
cht Monash Univer
202
Copyght Monash University
Monash Uni
onash Unive
opyright
essable
sity
Uni
ta
versity 202
ersity 2021.
sity 2021
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