7. Let a e R. Let S = {p(t), q(t), r(t)} be the subset of P2 withp(t)t2 +(a + 3)t +(a +3),q(t)r(t)(a – 3)t? + (a? – 9)t +(a – 3)t² +(а — 3),(а — 3)t + (а? — 9).|(a) Find all values of a for which S spans P2.(b) Let f(t) = t² +t+(a+3). Find all values of a for which f(t) belongs to Span S.

Since you have asked multiple question, we will solve the first question for you. If youwant any…

7. Let a E R. Let S = {p(t), q(t), r(t)} be the subset of P with t2 + p(t) q(t) r(t) (a + 3), (а — 3), (а — 3)t + (а2 - 9). (a + 3)t + (a – 3)t2 + (a² – 9)t + (a – 3)t2 + (a) Find all values of a for which S spans P2. (b) Let f(t) = t² +t+(a+3). Find all values of a for which f(t) belongs to Span S.

7. Let a E R. Let S = {p(t), q(t), r(t)} be the subset of P with t2 + p(t) q(t) r(t) (a + 3), (а — 3), (а — 3)t + (а2 - 9). (a + 3)t + (a – 3)t2 + (a² – 9)t + (a – 3)t2 + (a) Find all values of a for which S spans P2. (b) Let f(t) = t² +t+(a+3). Find all values of a for which f(t) belongs to Span S.

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

7. Let a e R. Let S = {p(t), q(t), r(t)} be the subset of P2 with
p(t)
t2 +
(a + 3)t +
(a +3),
q(t)
r(t)
(a – 3)t? + (a? – 9)t +
(a – 3)t² +
(а — 3),
(а — 3)t + (а? — 9).
|
(a) Find all values of a for which S spans P2.
(b) Let f(t) = t² +t+(a+3). Find all values of a for which f(t) belongs to Span S.

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