Is the set of polynomials {-1+ 3t – 21², 4 – 10t + 312, 4 – 8t – 212} independent? Answer this question directly without using a coordinate map. [Hint: Can you find scalars a,b, and c, not all zero, such that a (-1+3t – 21²) +b (4 – 101 + 3r²) + c (4 – 8t – 2r²) = 0 + 0t + Or². Collecting terms will again lead you to 3x3 linear system. Fell free to reuse some work from part (a) to save time!] If the answer is no (hint, it is), find a dependence relation for the polynomials. (Check your answer). Give a basis for the subspace H of P,, where H = span {-1+ 3t – 2t2, 4 – 10t + 3t?, 4 – 8t – 212}
Is the set of polynomials {-1+ 3t – 21², 4 – 10t + 312, 4 – 8t – 212} independent? Answer this question directly without using a coordinate map. [Hint: Can you find scalars a,b, and c, not all zero, such that a (-1+3t – 21²) +b (4 – 101 + 3r²) + c (4 – 8t – 2r²) = 0 + 0t + Or². Collecting terms will again lead you to 3x3 linear system. Fell free to reuse some work from part (a) to save time!] If the answer is no (hint, it is), find a dependence relation for the polynomials. (Check your answer). Give a basis for the subspace H of P,, where H = span {-1+ 3t – 2t2, 4 – 10t + 3t?, 4 – 8t – 212}
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:Problem 3: Consider the set of polynomials {-1+3t – 21², 4 – 10t + 3t², 4 – 8t – 21²} .
Let p¡(t) = – 1 + 3t – 21², p2(t) = 4 – 10t + 3ť², and p3(t) = 4 – 8t – 21². Let
H = span {p,(t), P2(t), P3(t)}, which is a subset of P,.
![Is the set of polynomials {-1+ 3t – 21², 4 – 10t + 31², 4 – 8t – 212} independent?
Answer this question directly without using a coordinate map.
[Hint: Can
you
find scalars a,b, and c, not all zero, such that
a (-1+3t – 2t²) +b (4 – 101 + 3t²) + c (4 – 8t – 2r²) = 0 + 0t + Or². Collecting
terms will again lead you to 3x3 linear system. Fell free to reuse some work from part (a)
to save time!]
If the answer is no (hint, it is), find a dependence relation for the polynomials. (Check
your answer).
Give a basis for the subspace H of P, where
21
H = span {-1+ 3t – 2t2, 4 – 10t + 3t?, 4 – 8t – 212}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb055c63f-89a3-4c28-8011-cd1d10eeedf8%2F3f156d83-d07d-4ca8-8226-ad70e9227866%2Fgg56r6j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Is the set of polynomials {-1+ 3t – 21², 4 – 10t + 31², 4 – 8t – 212} independent?
Answer this question directly without using a coordinate map.
[Hint: Can
you
find scalars a,b, and c, not all zero, such that
a (-1+3t – 2t²) +b (4 – 101 + 3t²) + c (4 – 8t – 2r²) = 0 + 0t + Or². Collecting
terms will again lead you to 3x3 linear system. Fell free to reuse some work from part (a)
to save time!]
If the answer is no (hint, it is), find a dependence relation for the polynomials. (Check
your answer).
Give a basis for the subspace H of P, where
21
H = span {-1+ 3t – 2t2, 4 – 10t + 3t?, 4 – 8t – 212}
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