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Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the structure of an inner product space by setting (f,g):= f(t)g(t)dt. Produce an orthonormal basis for V by applying the Gramm-Schmidt orthogonalisation process to the basis (1, x, x²) of V.

Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the structure of an inner product space by setting (f,g):= f(t)g(t)dt. Produce an orthonormal basis for V by applying the Gramm-Schmidt orthogonalisation process to the basis (1, x, x²) of V.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.CR: Review Exercises
Problem 73CR
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Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the structure of an inner product space by setting (f,g):= f(t)g(t)dt. Produce an orthonormal basis for V by applying the Gramm-Schmidt orthogonalisation process to the basis (1, x, x²) of V.
Transcribed Image Text:Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the structure of an inner product space by setting (f,g):= f(t)g(t)dt. Produce an orthonormal basis for V by applying the Gramm-Schmidt orthogonalisation process to the basis (1, x, x²) of V.
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