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Problem 4. Suppose the vector space V = P2, given the following set of basis B={1+², t-312, 1+t-t2}. and standard basis S = {1, t, t2}. 1 under B. (1)Find the coordinate of p(t) = 3t2 + 2t (2) Find the change-of-coordinates matrix from the basis B to the standard basis. (3) Find the change-of-coordinates matrix from the standard basis to the basis B.

Problem 4. Suppose the vector space V = P2, given the following set of basis B={1+², t-312, 1+t-t2}. and standard basis S = {1, t, t2}. 1 under B. (1)Find the coordinate of p(t) = 3t2 + 2t (2) Find the change-of-coordinates matrix from the basis B to the standard basis. (3) Find the change-of-coordinates matrix from the standard basis to the basis B.

Advanced Engineering Mathematics
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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a) (in image) with given set of basis (B) and standard basis (S) find coordinates of given p(t) b) find change of coordinates matrix from basis (B) to standard basis (S) c) find change of coordinates matrix from standard basis (S) to basis (B)
Problem 4. Suppose the vector space V = P2, given the following set of basis and standard basis B={1+t2, t-312, 1+t-t2}. S = {1, t, t2}. (1)Find the coordinate of p(t) = 3t2 + 2t - 1 under B. (2) Find the change-of-coordinates matrix from the basis B to the standard basis. (3) Find the change-of-coordinates matrix from the standard basis to the basis B.
Transcribed Image Text:Problem 4. Suppose the vector space V = P2, given the following set of basis and standard basis B={1+t2, t-312, 1+t-t2}. S = {1, t, t2}. (1)Find the coordinate of p(t) = 3t2 + 2t - 1 under B. (2) Find the change-of-coordinates matrix from the basis B to the standard basis. (3) Find the change-of-coordinates matrix from the standard basis to the basis B.
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