32. Let p, (t) = 1 +t², p2(t) = t – 3t², p3(t) = 1 +t – 3t2. || - - a. Use coordinate vectors to show that these polynomials form a basis for P2. b. Consider the basis B = {p1,P2, P3} for P2. Find q in P2, given that [q]B 1
32. Let p, (t) = 1 +t², p2(t) = t – 3t², p3(t) = 1 +t – 3t2. || - - a. Use coordinate vectors to show that these polynomials form a basis for P2. b. Consider the basis B = {p1,P2, P3} for P2. Find q in P2, given that [q]B 1
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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![32. Let p, (t) = 1+t², p2(t) = t – 3t², p3(t) = 1 + t – 3t².
%3D
|
a. Use coordinate vectors to show that these polynomials
form a basis for P2.
b. Consider the basis B = {p, P2, P3} for P2. Find q in P2,
given that [g]B
1
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F198e9535-3c41-410b-8bb1-68969a8c24fc%2F45125014-8e5d-4aec-be79-02911e8d1785%2Fh53nlsf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:32. Let p, (t) = 1+t², p2(t) = t – 3t², p3(t) = 1 + t – 3t².
%3D
|
a. Use coordinate vectors to show that these polynomials
form a basis for P2.
b. Consider the basis B = {p, P2, P3} for P2. Find q in P2,
given that [g]B
1
2
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