3. Let p₁(x) = ½x(x − 1), p2(x) = −x² + 1 and p3(x) = ½x(x+1).-(a) Show that E = {P1, P2, P3} is a basis for P2.(b) Find the coordinates of q(x) = 2x² - 3x+7 relative to the basis E. (Hint:Consider q(-1), q(0) and q(1).)

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Answered: 3. Let p₁(x) = ½x(x − 1), p2(x) = −x² +…

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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3. Let p₁(x) = ½x(x − 1), p2(x) = −x² + 1 and p3(x) = ½x(x+1). - (a) Show that E = {P1, P2, P3} is a basis for P2. (b) Find the coordinates of q(x) = 2x² - 3x+7 relative to the basis E. (Hint: Consider q(-1), q(0) and q(1).)