a) Let q(t) = 4t2 + 2t + 9 be an element of P2. Write the coorfinate vector of q(t) relative to standard basis of P2. (Recall that the standard basis of P2 is E = {1,t,t2}.) b) Use coordinate vectors to determine if the following polynomial are linearly inpendent in P2 c) Is P2= R3? Justify your answer

a) Let q(t) = 4t2 + 2t + 9 be an element of P2. Write the coorfinate vector of q(t) relative to standard basis of P2. (Recall that the standard basis of P2 is E = {1,t,t2}.) b) Use coordinate vectors to determine if the following polynomial are linearly inpendent in P2 c) Is P2= R3? 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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Question

a) Let q(t) = 4t² + 2t + 9 be an element of P₂. Write the coorfinate vector of q(t) relative to standard basis of P₂. (Recall that the standard basis of P₂ is E = {1,t,t²}.)

b) Use coordinate vectors to determine if the following polynomial are linearly inpendent in P₂

c) Is P₂= R³? Justify your answer

P1(t) = 1- 31+², Pa(t) =-1+ 4t + t², Pa(t)=-2+ 10t + 61²

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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