Explanation Given: The given set is { 1 + α x 2 , 1 + x + x 2 , 2 + x } . Approach: A set S is basis for P 2 ( ℝ ) when all the vectors of the set are linearly independent. The vectors are linearly independent only if W [ p 1 , p 2 , p 3 ] ( x ) ≠ 0 . Calculation: Let, p 1 ( x ) = 1 + α x 2 , p 2 ( x ) = 1 + x + x 2 , and p 3 ( x ) = 2 + x The Wronskian will be given as, W [ p 1 , p 2 , p 3 ] ( x ) = | 1 + α x 2 1 + x + x 2 2 + x 2 α x 1 + 2 x 1 2 α 2 0 | = ( 1 + α x 2

Differential Equations and Linear Algebra (4th Edition)

4th Edition

ISBN: 9780321964670

Author: Stephen W. Goode, Scott A. Annin

Publisher: PEARSON

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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Chapter 4.6, Problem 36P

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The values of the constant α for which {1+αx2,1+x+x2,2+x} is a basis for P2(ℝ).

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Chapter 4.6, Problem 35P

Chapter 4.6, Problem 37P

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Differential Equations and Linear Algebra (4th Edition)

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The values of the constant α for which { 1 + α x 2 , 1 + x + x 2 , 2 + x } is a basis for P 2 ( ℝ ) .

Solution Summary: The author explains how the constant alpha is a basis for P_2(R) when all the vectors of the set are linearly independent

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To find:

The values of the constant α for which {1+αx2,1+x+x2,2+x} is a basis for P2(ℝ).

Want to see the full answer?

Chapter 4 Solutions

The values of the constant α for which { 1 + α x 2 , 1 + x + x 2 , 2 + x } is a basis for P 2 ( ℝ ) .

Solution Summary: The author explains how the constant alpha is a basis for P_2(R) when all the vectors of the set are linearly independent

Concept explainers

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To find: The values of the constant α for which {1+αx2,1+x+x2,2+x} is a basis for P2(ℝ).

Want to see the full answer?

Chapter 4 Solutions

To find:

The values of the constant α for which {1+αx2,1+x+x2,2+x} is a basis for P2(ℝ).