Both sets below are bases for P,: P = {pj, P2, P3} = {1+r?, 1+21, t + 21²} Q = {q,, 42» 93} = {1+3t + 2r², 4 + 5t – 1², – 1 – 41 +1?} (a) Find [1+3t + 2t²| That is, find |91, P (b) Using the same idea from problem (a), "simultaneously" find [1 + 3r + 2r*|, [4 +5t – 1°,, and [-1– 41 +r²],: (c) Write the change-of-coordinates matrix from Q to P. That is, find the matrix PP-0 that such Po-e la + bt +ct*]. = [a + bt + cr*],. P-Q Q (d) Find [9+23t|: (e) Use your matrix from part (c) and matrix-vector multiplication to find 9+ 23t||
Both sets below are bases for P,: P = {pj, P2, P3} = {1+r?, 1+21, t + 21²} Q = {q,, 42» 93} = {1+3t + 2r², 4 + 5t – 1², – 1 – 41 +1?} (a) Find [1+3t + 2t²| That is, find |91, P (b) Using the same idea from problem (a), "simultaneously" find [1 + 3r + 2r*|, [4 +5t – 1°,, and [-1– 41 +r²],: (c) Write the change-of-coordinates matrix from Q to P. That is, find the matrix PP-0 that such Po-e la + bt +ct*]. = [a + bt + cr*],. P-Q Q (d) Find [9+23t|: (e) Use your matrix from part (c) and matrix-vector multiplication to find 9+ 23t||
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 = {Pj, P2, P3} = {1+t², 1+2t, t + 21?}
Q = {q,, 92, 93} = {1+3t +2r?, 4 + 5t – r?, – 1 – 4t + t²}
(a) Find [1+3t + 2r²] · That is, find [q1):
P
(b) Using the same idea from problem (a), “simultaneously" find
[1 + 3t + 2r*] „ • [4 + 5t – 1²],
and [-1 – 41 + r²] ,
(c) Write the change-of-coordinates matrix from Q to P. That is, find the matrix Po such
that
P-Q
Pg-6 la + bt + ct], = [a + bt + ct],
PEQ
Q
(d) Find 9+ 231]
(e) Use your matrix from part (c) and matrix-vector multiplication to find 9 + 23t|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe7fbfd5-7c05-4bbb-a7af-d53de29b113b%2F299a51a6-23ae-4782-9564-94c63d39cefa%2Ftfj4q9s_processed.png&w=3840&q=75)
Transcribed Image Text:Both sets below are bases for P,:
P = {Pj, P2, P3} = {1+t², 1+2t, t + 21?}
Q = {q,, 92, 93} = {1+3t +2r?, 4 + 5t – r?, – 1 – 4t + t²}
(a) Find [1+3t + 2r²] · That is, find [q1):
P
(b) Using the same idea from problem (a), “simultaneously" find
[1 + 3t + 2r*] „ • [4 + 5t – 1²],
and [-1 – 41 + r²] ,
(c) Write the change-of-coordinates matrix from Q to P. That is, find the matrix Po such
that
P-Q
Pg-6 la + bt + ct], = [a + bt + ct],
PEQ
Q
(d) Find 9+ 231]
(e) Use your matrix from part (c) and matrix-vector multiplication to find 9 + 23t|
![Both sets below are bases for P,:
P = {Pj, P2, P3} = {1+t², 1+2t, t + 21?}
Q = {q,, 92, 93} = {1+3t +2r?, 4 + 5t – r?, – 1 – 4t + t²}
(a) Find [1+3t + 2r²] · That is, find [q1):
P
(b) Using the same idea from problem (a), “simultaneously" find
[1 + 3t + 2r*] „ • [4 + 5t – 1²],
and [-1 – 41 + r²] ,
(c) Write the change-of-coordinates matrix from Q to P. That is, find the matrix Po such
that
P-Q
Pg-6 la + bt + ct], = [a + bt + ct],
PEQ
Q
(d) Find 9+ 231]
(e) Use your matrix from part (c) and matrix-vector multiplication to find 9 + 23t|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe7fbfd5-7c05-4bbb-a7af-d53de29b113b%2F299a51a6-23ae-4782-9564-94c63d39cefa%2Fpzhu1hc_processed.png&w=3840&q=75)
Transcribed Image Text:Both sets below are bases for P,:
P = {Pj, P2, P3} = {1+t², 1+2t, t + 21?}
Q = {q,, 92, 93} = {1+3t +2r?, 4 + 5t – r?, – 1 – 4t + t²}
(a) Find [1+3t + 2r²] · That is, find [q1):
P
(b) Using the same idea from problem (a), “simultaneously" find
[1 + 3t + 2r*] „ • [4 + 5t – 1²],
and [-1 – 41 + r²] ,
(c) Write the change-of-coordinates matrix from Q to P. That is, find the matrix Po such
that
P-Q
Pg-6 la + bt + ct], = [a + bt + ct],
PEQ
Q
(d) Find 9+ 231]
(e) Use your matrix from part (c) and matrix-vector multiplication to find 9 + 23t|
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