Given two bases B = {(−1, −1,2), (−1, −2,3), (1, −6, 6)} V1 V2 U1 and C = {(1, −1, −1), (−1, −1,1), (1, —2,1)} V3 22 uz of R³, (i) find the change of coordinates (transition) matrix ÂMc € R³×³ from the coordinates with respect to C to the coordinates with respect to B, (ii) find the coordinates [p(x)] € R³ and [p(x)]c € R³ of p(x) = 3x² − x + 4 € P3, with respect to B and C, (iii) verify the equality ßMc[p(x)]c = [p(x)]ß. Justify your answer!
Given two bases B = {(−1, −1,2), (−1, −2,3), (1, −6, 6)} V1 V2 U1 and C = {(1, −1, −1), (−1, −1,1), (1, —2,1)} V3 22 uz of R³, (i) find the change of coordinates (transition) matrix ÂMc € R³×³ from the coordinates with respect to C to the coordinates with respect to B, (ii) find the coordinates [p(x)] € R³ and [p(x)]c € R³ of p(x) = 3x² − x + 4 € P3, with respect to B and C, (iii) verify the equality ßMc[p(x)]c = [p(x)]ß. Justify your answer!
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Given two bases
B = {(−1, −1, 2), (−1, −2,3), (1, −6, 6)}
V1
V2
21
and
C = {(1,−1, −1), (−1, −1,1), (1, −2,1)}
V3
U2
Uz
of IR³,
(i) find the change of coordinates (transition) matrix BMc € R³×³ from the
coordinates with respect to C to the coordinates with respect to B,
(ii) find the coordinates [p(x)]3 € R³ and [p(x)]c € R³ of
p(x) = 3x² − x + 4 € P3, with respect to B and C,
-
(iii) verify the equality ßMc[p(x)]c = [p(x)]ß.
Justify your answer!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc5779d6d-aa05-4ad7-80c7-ed0d0a2afe0f%2F42b245b3-f069-4fbd-b543-d245dd10e13c%2Fni3rdj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given two bases
B = {(−1, −1, 2), (−1, −2,3), (1, −6, 6)}
V1
V2
21
and
C = {(1,−1, −1), (−1, −1,1), (1, −2,1)}
V3
U2
Uz
of IR³,
(i) find the change of coordinates (transition) matrix BMc € R³×³ from the
coordinates with respect to C to the coordinates with respect to B,
(ii) find the coordinates [p(x)]3 € R³ and [p(x)]c € R³ of
p(x) = 3x² − x + 4 € P3, with respect to B and C,
-
(iii) verify the equality ßMc[p(x)]c = [p(x)]ß.
Justify your answer!
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