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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
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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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.
Transcribed Image Text: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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