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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.3: Algebraic Expressions

Problem 32E

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**Problem Statement:**

Let \( P_2 \) be the vector space of polynomials of degree at most 2. Determine the coordinates of the polynomial \( p(x) = x + x^2 - 2 \) relative to the basis \( B = \{1, x - 2, x^2 - x\} \).

**Explanation:**

We need to express the polynomial \( p(x) = x + x^2 - 2 \) in terms of the basis \( B \). This requires us to find the coefficients \( c_1, c_2, \) and \( c_3 \) such that:

\[ p(x) = c_1 \cdot 1 + c_2 \cdot (x - 2) + c_3 \cdot (x^2 - x) \]

where \( 1, (x - 2), \) and \( (x^2 - x) \) form the basis \( B \).

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