Question Consider the vector space P, consisting of all 2 polynomials of degree at most two together with the zero polynomial. Let S = {p₁(t), p₂(t), p₂(t)} be a set of 3 polynomials in P, where p₁(t) = −3t²−7t+6, p₂(t)=6t²-6t-2, P3(t)= −7t²+3t+6 Determine whether, or not, the set S (a) is linearly independent in P,? 2 (b) polynomial p₂(t) belongs to span {p, (t), p₂(t)}. Determine whether, or not, the
Question Consider the vector space P, consisting of all 2 polynomials of degree at most two together with the zero polynomial. Let S = {p₁(t), p₂(t), p₂(t)} be a set of 3 polynomials in P, where p₁(t) = −3t²−7t+6, p₂(t)=6t²-6t-2, P3(t)= −7t²+3t+6 Determine whether, or not, the set S (a) is linearly independent in P,? 2 (b) polynomial p₂(t) belongs to span {p, (t), p₂(t)}. Determine whether, or not, the
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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Transcribed Image Text:Question
Consider the vector space P consisting of all
2
polynomials of degree at most two together with
the zero polynomial.
Let S = {p₁(t), p₂(t), p²(t)} be a set of 3
polynomials in P, where
p₁(t) = -31²-7t+6, p₂(t)=61²-61-2, p₂(t)=-71² +3t+6
Determine whether, or not, the set S
(a)
is linearly independent in P₂?
(b)
Determine whether, or not, the
polynomial p₂(t) belongs to
P3
span {p,(t), p₂(t)}
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