Both sets below are bases for P,: P = {P), P2. P3} = {1+r?, 1+2t, t + 21²} Q = {q,• 92, 93} = {1+3t +2r², 4 + 5t – 1², – 1– 4t +1?} (g) Find the change-of-coordinates matrix from P to Q. That is, find the matrix Po-g such that Pa-9 la +bt + ct², = [a + bt + ct*]. 3 (h) There is a degree two polynomial, f (t), such that f (t). Use matrix-vector 6. multiplication to find [f (t)]: (i) Find the polynomial f (t) from part (h). Your final answer should be in the form f (t) = a + bt +ct² , with a, b, and c real numbers.
Both sets below are bases for P,: P = {P), P2. P3} = {1+r?, 1+2t, t + 21²} Q = {q,• 92, 93} = {1+3t +2r², 4 + 5t – 1², – 1– 4t +1?} (g) Find the change-of-coordinates matrix from P to Q. That is, find the matrix Po-g such that Pa-9 la +bt + ct², = [a + bt + ct*]. 3 (h) There is a degree two polynomial, f (t), such that f (t). Use matrix-vector 6. multiplication to find [f (t)]: (i) Find the polynomial f (t) from part (h). Your final answer should be in the form f (t) = a + bt +ct² , with a, b, and c real numbers.
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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![Both sets below are bases for P,:
P = {p1, P2, P3} = {1+1?, 1+ 2t, t + 2t²}
Q = {q,, 42 q3} = {1+3t + 2r², 4 + 5t – 1?, – 1 – 41 +1?}
%3D
Find the change-of-coordinates matrix from P to Q. That is, find the matrix Po-g such
that
Q+P
Pa-9 la + bt + ct°],- [a + bt + cr°],
Q
3
(h) There is a degree two polynomial, f (t), such that f (t).
Use matrix-vector
P
multiplication to find [f (t)]
(i) Find the polynomial f (t) from part (h). Your final answer should be in the form
f (t) = a + bt + ct² , with a, b, and c real numbers.
а,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe7fbfd5-7c05-4bbb-a7af-d53de29b113b%2F9bd47737-ddd1-4739-9761-be1b5ed9815c%2F3qxu2z_processed.png&w=3840&q=75)
Transcribed Image Text:Both sets below are bases for P,:
P = {p1, P2, P3} = {1+1?, 1+ 2t, t + 2t²}
Q = {q,, 42 q3} = {1+3t + 2r², 4 + 5t – 1?, – 1 – 41 +1?}
%3D
Find the change-of-coordinates matrix from P to Q. That is, find the matrix Po-g such
that
Q+P
Pa-9 la + bt + ct°],- [a + bt + cr°],
Q
3
(h) There is a degree two polynomial, f (t), such that f (t).
Use matrix-vector
P
multiplication to find [f (t)]
(i) Find the polynomial f (t) from part (h). Your final answer should be in the form
f (t) = a + bt + ct² , with a, b, and c real numbers.
а,
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