In P2, find the change-of-coordinates matrix from the basis B = {1+ 3t², -3 +t-8t²,1 - 4t) to the standard basis. Then write t² as a linear combination of the polynomials in B. In P2₁ find the change-of-coordinates matrix from the basis B to the standard basis. P = C+B (Simplify your answer.) Write t² as a linear combination of the polynomials in B. +²=(1+31²)+(-3+1-8²)+(1-4t) [ (Simplify your answers.)
In P2, find the change-of-coordinates matrix from the basis B = {1+ 3t², -3 +t-8t²,1 - 4t) to the standard basis. Then write t² as a linear combination of the polynomials in B. In P2₁ find the change-of-coordinates matrix from the basis B to the standard basis. P = C+B (Simplify your answer.) Write t² as a linear combination of the polynomials in B. +²=(1+31²)+(-3+1-8²)+(1-4t) [ (Simplify your answers.)
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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Transcribed Image Text:In P2, find the change-of-coordinates
matrix from the basis B = {1+ 3t², -3 +t - 8t²,1 - 4t) to the standard basis.
Then write t² as a linear combination of the polynomials in B.
In P2₁
find the change-of-coordinates matrix from the basis B to the standard basis.
P =
C+B
(Simplify your answer.)
Write t² as a linear combination of the polynomials in B.
+²=(1+31²)+(-3+1-8²)+(1-4t)
(Simplify your answers.)
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