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7. Consider the inner product defined on P₂ by (p, q) = p(-1)q(−1) + p(0)q(0) + p(1)q(1). f₁(x) = x − x², ƒ₂(x) = 1 - x, and let WC P₂ be the Consider the two linearly independent span of B = {f₁, f2}. at polynomials f (a) Apply the Gram-Schmidt algorithm to the basis B to produce a new basis B' orthonormal with respect to the above inner product. (b) Express rЄ W as a linear combination of the elements of B', where r(x) = −2+3x − x². = {91,92} which is

7. Consider the inner product defined on P₂ by (p, q) = p(-1)q(−1) + p(0)q(0) + p(1)q(1). f₁(x) = x − x², ƒ₂(x) = 1 - x, and let WC P₂ be the Consider the two linearly independent span of B = {f₁, f2}. at polynomials f (a) Apply the Gram-Schmidt algorithm to the basis B to produce a new basis B' orthonormal with respect to the above inner product. (b) Express rЄ W as a linear combination of the elements of B', where r(x) = −2+3x − x². = {91,92} which is

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7. Consider the inner product defined on P₂ by (p, q) = p(−1)q(−1) +p(0)q(0) +p(1)q(1). Sum of D - the fall independent, polynomials / (+) - (2) — 12, at et WP; be the span B = {f₁, f2}. {91, 92} which is (a) Apply the Gram-Schmidt algorithm to the basis B to produce a new basis B' orthonormal with respect to the above inner product. (b) Express r € W as a linear combination of the elements of B', where r(x) = −2+ 3x − x². =
Transcribed Image Text:7. Consider the inner product defined on P₂ by (p, q) = p(−1)q(−1) +p(0)q(0) +p(1)q(1). Sum of D - the fall independent, polynomials / (+) - (2) — 12, at et WP; be the span B = {f₁, f2}. {91, 92} which is (a) Apply the Gram-Schmidt algorithm to the basis B to produce a new basis B' orthonormal with respect to the above inner product. (b) Express r € W as a linear combination of the elements of B', where r(x) = −2+ 3x − x². =
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