Let {u1 (x) = 12, u2 (x) = 12x, u3 (x) = 8x² } be a basis for a subspace of P2. Use the Gram-Schmidt 1 process to find an orthogonal basis under the integration inner product (f,g) = | f(x)g(x) dx on C[0, 1]. Orthogonal basis: {v1(x) = 12, v2 (x) 12x + a, v3 (x) = 8x² + bx +c} а 3D Еx: 1.23 3 Ex: 1.23 : с — Еx: 1.23 3

Let {u1 (x) = 12, u2 (x) = 12x, u3 (x) = 8x² } be a basis for a subspace of P2. Use the Gram-Schmidt 1 process to find an orthogonal basis under the integration inner product (f,g) = | f(x)g(x) dx on C[0, 1]. Orthogonal basis: {v1(x) = 12, v2 (x) 12x + a, v3 (x) = 8x² + bx +c} а 3D Еx: 1.23 3 Ex: 1.23 : с — Еx: 1.23 3

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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Linear Algebra

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 under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Let {u1 (x) = 12, u2 (x) =
12x, uz (x) = 8x2 } be a basis for a subspace of P2. Use the Gram-Schmidt
process to find an orthogonal basis under the integration inner product (f, g)
f(x)g(x) dæ on C[0, 1].
Orthogonal basis: {v1(x) = 12, v2 (x)
12x + a, v3 (x) = 8x² + bx +c}
=
а —D Еx: 1.23
b
= Ex: 1.23
с — Еx: 1.23

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