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).)

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).)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...

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Question

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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