Consider the vector space V, of polynomials of degree less than or equal to 3 that do not have terms in t or t^2, that is, v ∈ V if v = p(t) = a⋅1+b⋅t+c⋅t2+d ⋅t3, with the constraint b = c = 0.For this space, consider the basesα = {e1 = 1 + 0 ⋅ t + 0 ⋅ t2 + 0 ⋅ t3, e2 = 0 + 0 ⋅ t + 0 ⋅ t2 + 1 ⋅ t3}andβ = {v1 = 1 + 0 ⋅ t + 0 ⋅ t2 + 1 ⋅ t3, v2 = 1 + 0 ⋅ t + 0 ⋅ t2 + 0 ⋅ t3}Choose one or more options: O The. ifv E Vs the polynomial whose representationin the baseßlt's[then[ v]a5O B. The base change matrix ofaforßlt's[1; = |1|Ç.The base change matrix ofßforalt's[ 1% = |-O d. ifv E Vis the polynomial whose representation inthe base alts f]). = hen olg =3thenſ o)athe base alt's[ v]a2|

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Consider the vector space V, of polynomials of degree less than or equal to 3 that do not have terms in t or t^2, that is, v ∈ V if v = p(t) = a⋅1+b⋅t+c⋅t2+d ⋅t3, with the constraint b = c = 0. For this space, consider the bases α = {e1 = 1 + 0 ⋅ t + 0 ⋅ t2 + 0 ⋅ t3, e2 = 0 + 0 ⋅ t + 0 ⋅ t2 + 1 ⋅ t3} and β = {v1 = 1 + 0 ⋅ t + 0 ⋅ t2 + 1 ⋅ t3, v2 = 1 + 0 ⋅ t + 0 ⋅ t2 + 0 ⋅ t3} Choose one or more options:

Consider the vector space V, of polynomials of degree less than or equal to 3 that do not have terms in t or t^2, that is, v ∈ V if v = p(t) = a⋅1+b⋅t+c⋅t2+d ⋅t3, with the constraint b = c = 0. For this space, consider the bases α = {e1 = 1 + 0 ⋅ t + 0 ⋅ t2 + 0 ⋅ t3, e2 = 0 + 0 ⋅ t + 0 ⋅ t2 + 1 ⋅ t3} and β = {v1 = 1 + 0 ⋅ t + 0 ⋅ t2 + 1 ⋅ t3, v2 = 1 + 0 ⋅ t + 0 ⋅ t2 + 0 ⋅ t3} Choose one or more options:

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

Consider the vector space V, of polynomials of degree less than or equal to 3 that do not have terms in t or t^2, that is, v ∈ V if v = p(t) = a⋅1+b⋅t+c⋅t2+d ⋅t3, with the constraint b = c = 0.

For this space, consider the bases
α = {e1 = 1 + 0 ⋅ t + 0 ⋅ t2 + 0 ⋅ t3, e2 = 0 + 0 ⋅ t + 0 ⋅ t2 + 1 ⋅ t3}

and

β = {v1 = 1 + 0 ⋅ t + 0 ⋅ t2 + 1 ⋅ t3, v2 = 1 + 0 ⋅ t + 0 ⋅ t2 + 0 ⋅ t3}

Choose one or more options:

O The. ifv E Vs the polynomial whose representation
in the baseßlt's[
then[ v]a
5
O B. The base change matrix ofaforßlt's
[1; = |
1
|
Ç.
The base change matrix ofßforalt's
[ 1% = |
-
O d. ifv E Vis the polynomial whose representation in
the base alts f]). = hen olg =
3
thenſ o)a
the base alt's[ v]a
2
|

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