Given P₂={a+at+a₂t² B = {1-t², t+t², 2-t-t²} and E= {1, t, t²} [1] Show that {1-12, t+t², 2-t-t²} are linearly independent. Show all support work. | a, ª, a are reals } [2] Find the change-of-coordinate matrix from E to B PE-B ▲ write all entries in exact form, show support work. [3] Find the E-coordinates of q(t) given that [4]B = 2 using change-coordinate-matrix. -3 3 Show work to justify your answer.
Given P₂={a+at+a₂t² B = {1-t², t+t², 2-t-t²} and E= {1, t, t²} [1] Show that {1-12, t+t², 2-t-t²} are linearly independent. Show all support work. | a, ª, a are reals } [2] Find the change-of-coordinate matrix from E to B PE-B ▲ write all entries in exact form, show support work. [3] Find the E-coordinates of q(t) given that [4]B = 2 using change-coordinate-matrix. -3 3 Show work to 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
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![Given P₂ = { a+at+at² | ª, ª, a are reals }
B = {1-1², t+t², 2-t-t²} and E= {1, t, 1²}
[1] Show that {1-t², t+t², 2-t-t²} are linearly independent. Show all support work.
[2] Find the change-of-coordinate matrix from & to B PE-B
▲ write all entries in exact form, show support work.
[3] Find the E-coordinates of q(t) given that [9]B 2 using change-coordinate-matrix.
-131
Show work to justify your answer.
[4] Find the B-coordinates of p(t) = -4+t+t² using change-coordinate-matrix.
Show work to justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a62179c-1d7b-45f7-8f2c-358abb207063%2Fe751d4c8-578f-4d0b-8e9f-c7316c76739f%2Fx4rk84q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given P₂ = { a+at+at² | ª, ª, a are reals }
B = {1-1², t+t², 2-t-t²} and E= {1, t, 1²}
[1] Show that {1-t², t+t², 2-t-t²} are linearly independent. Show all support work.
[2] Find the change-of-coordinate matrix from & to B PE-B
▲ write all entries in exact form, show support work.
[3] Find the E-coordinates of q(t) given that [9]B 2 using change-coordinate-matrix.
-131
Show work to justify your answer.
[4] Find the B-coordinates of p(t) = -4+t+t² using change-coordinate-matrix.
Show work to justify your answer.
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