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In P2₁ find the change-of-coordinates matrix from the basis B = { 1 + 5t²,3 +t+16t²,1 - 6t} to the standard basis. Then write t² as a linear combination of the polynomials in B. In P2, find the change-of-coordinates matrix from the basis B to the standard basis. P = C+B (Simplify your answer.)

In P2₁ find the change-of-coordinates matrix from the basis B = { 1 + 5t²,3 +t+16t²,1 - 6t} to the standard basis. Then write t² as a linear combination of the polynomials in B. In P2, find the change-of-coordinates matrix from the basis B to the standard basis. P = C+B (Simplify your answer.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
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In P2, find the change-of-coordinates matrix from the basis B = {1 + 5t²,3 + t + 16t²,1 − 6t} to the standard basis. Then write t² as a linear combination of the polynomials in B. In P2, find the change-of-coordinates matrix from the basis B to the standard basis. P = C-B (Simplify your answer.)
Transcribed Image Text:In P2, find the change-of-coordinates matrix from the basis B = {1 + 5t²,3 + t + 16t²,1 − 6t} to the standard basis. Then write t² as a linear combination of the polynomials in B. In P2, find the change-of-coordinates matrix from the basis B to the standard basis. P = C-B (Simplify your answer.)
In P2, the standard basis C = {1,t,t2}. Then find the B-coordinate vector for 1 - 2t + 2t². find the change-of-coordinates matrix from the basis B = {1 - 2t + t²,4 - 7t + 5t²,3 − 4t + 6t²} to In P2, find the change-of-coordinates matrix from the basis B = {1-2t+t²,4-7t + 512²,3-4t+ 6t²} to the standard basis C = = {1,t,t²}. 1 4 3 P = -2 -7 -4 C-B 1 5 6 (Simplify your answer.) Find the B-coordinate vector for 1-2t+2t². [X] B = (Simplify your answer.)
Transcribed Image Text:In P2, the standard basis C = {1,t,t2}. Then find the B-coordinate vector for 1 - 2t + 2t². find the change-of-coordinates matrix from the basis B = {1 - 2t + t²,4 - 7t + 5t²,3 − 4t + 6t²} to In P2, find the change-of-coordinates matrix from the basis B = {1-2t+t²,4-7t + 512²,3-4t+ 6t²} to the standard basis C = = {1,t,t²}. 1 4 3 P = -2 -7 -4 C-B 1 5 6 (Simplify your answer.) Find the B-coordinate vector for 1-2t+2t². [X] B = (Simplify your answer.)
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