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
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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Transcribed Image Text: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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