Let P2 be the vector space of all real polynomials of degree at most 2. Let P1, P2, P3 Є P2 be given by p₁(x) = 3x, p2(x) = 2x + x², and p3(x) = ẞ+ax². a) (4 marks) Find the condition on a, ẞ ER that ensures that {P1, P2, P3} is a basis for P2. (You are free to assume that the polynomials 1, x and x² are linearly independent.) = b) (2 marks) In the case ẞ combination of P1, P2 and P3. 1, write the polynomial p(x) = 1 − x - 1½ x² as a linear

Let P2 be the vector space of all real polynomials of degree at most 2. Let P1, P2, P3 Є P2 be given by p₁(x) = 3x, p2(x) = 2x + x², and p3(x) = ẞ+ax². a) (4 marks) Find the condition on a, ẞ ER that ensures that {P1, P2, P3} is a basis for P2. (You are free to assume that the polynomials 1, x and x² are linearly independent.) = b) (2 marks) In the case ẞ combination of P1, P2 and P3. 1, write the polynomial p(x) = 1 − x - 1½ x² as a linear

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 44EQ

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