Let f1(x) = − 1 6 (x − 1)(x − 2)(x − 3), f2(x) = 1 2 x(x − 2)(x − 3), f3(x) = − 1 2 x(x − 1)(x − 3) and f4(x) = 1 6 x(x − 1)(x − 2). (i) Prove that B = (f1, f2, f3, f4) is a basis for P3[x], the vector space of all polynomials of degree at most three.

Let f1(x) = − 1 6 (x − 1)(x − 2)(x − 3), f2(x) = 1 2 x(x − 2)(x − 3), f3(x) = − 1 2 x(x − 1)(x − 3) and f4(x) = 1 6 x(x − 1)(x − 2). (i) Prove that B = (f1, f2, f3, f4) is a basis for P3[x], the vector space of all polynomials of degree at most three.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.5: Systems Of Linear Equations In More Than Two Variables

Problem 43E

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Question

. Let f1(x) = − 1 6 (x − 1)(x − 2)(x − 3), f2(x) = 1 2 x(x − 2)(x − 3), f3(x) = − 1 2 x(x − 1)(x − 3) and f4(x) = 1 6 x(x − 1)(x − 2). (i) Prove that B = (f1, f2, f3, f4) is a basis for P3[x], the vector space of all polynomials of degree at most three.

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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