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Consider the inner product space P2 (R) with (f,g) = f(x)g(x)da for every f, g € P2 (R). Construct the orthogonal basis using the Gram-Schmidt algorithm that results from the standard basis B = (1, x, x²). {1, x, x²} {1, x1, x²-a 000 0. 1x1 }} {1, x − 1/1, x² - = x + } } {1, x1,x²-x+1}

Consider the inner product space P2 (R) with (f,g) = f(x)g(x)da for every f, g € P2 (R). Construct the orthogonal basis using the Gram-Schmidt algorithm that results from the standard basis B = (1, x, x²). {1, x, x²} {1, x1, x²-a 000 0. 1x1 }} {1, x − 1/1, x² - = x + } } {1, x1,x²-x+1}

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 37EQ
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Consider the inner product space P₂(R) with (f, g) = f(x)g(x)da for every f,9 € P₂ (R). Construct the orthogonal basis using the Gram-Schmidt algorithm that results from the standard basis B = (1, x, x²). {1, x, x²} {1, x − 21/1, x² - {1, x − 1/1, x² 29 - X T - }} x + {1, x − 1/1, x² - x + - 2⁹ x + } }
Transcribed Image Text:Consider the inner product space P₂(R) with (f, g) = f(x)g(x)da for every f,9 € P₂ (R). Construct the orthogonal basis using the Gram-Schmidt algorithm that results from the standard basis B = (1, x, x²). {1, x, x²} {1, x − 21/1, x² - {1, x − 1/1, x² 29 - X T - }} x + {1, x − 1/1, x² - x + - 2⁹ x + } }
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