Show that if { (, (1, . . . , (n} is an orthogonal set of functions

Question:

Show that if { (, (1, . . . , (n} is an orthogonal set of functions on [a, b] with respect to the weight function w, then {(0, (1, . . . , (n} is a linearly independent set.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Numerical Analysis

ISBN: 978-0538733519

9th edition

Authors: Richard L. Burden, J. Douglas Faires

See More Books

Question Posted: Mar 22, 2016 03:00 AM

See More Questions

Use the Laguerre polynomials calculated in Exercise 11 to compute the least squares polynomials of degree one, two, and three on the interval (0,) with respect to the weight function w(x) = ex for...
These orthogonal polynomials are defined by H eo (1) = 1 and As is true for many special functions, the literature contains more than one notation, and one sometimes defines as Hermite polynomials...
Find the eigenvalues and eigenfunctions. Verify orthogonality. Start by writing the ODE in the form (1), using Prob. 6. Show details of your work. Orthogonal polynomials play a great role in...
Match the items below by entering the appropriate code letter in the space provided. An entry that involves three or more accounts Transferring journal entries to ledger accounts The side which...
The Kumar Corporation, a firm in the 34 percent marginal tax bracket with a 15 percent required rate of return or discount rate, is considering a new project. This project involves the introduction...
Describe how budgets may be helpful for methods improvement in restaurant operations. What kinds of information would you hope to gain from the budgets?
Consider the inspection described in Example 2.11. Six parts are selected randomly from a bin of 50 parts, but assume that the selected part is replaced before the next one is selected. The bin...
Santana Rey, owner of Business Solutions, realizes that she needs to begin accounting for bad debts expense. Assume that Business Solutions has total revenues of $44,000 during the first three months...
A linear time-invariant filter is described by the difference equation y[n] = x[n]+x[n-1] x[n - 3] - x[n 4] (a) Derive a simple expression for H(), the frequency response of this system. (b) Sketch...
Great Ape Glassworks manufactures glass used for the screens on smartphones. It has two producing departments, P1 and P2, and only one service department, S1. The company is able to track overhead to...
Suppose {(0, (1. . . (n} is any linearly independent set in ((n. Show that for any element Q (n, there exist unique constants c0, c1, . . . , cn, such that Qx) = Crt (x). k=0
Show that the normal equations (8.6) have a unique solution. [Show that the only solution for the function f (x) 0 is aj = 0, j = 0, 1. . . n. Multiply Eq. (8.6) by aj , and sum over all j....
Compute each of the following. (1 + 0.08) 10
Does the average investors willingness to take on risk vary over time? Explain.
Should companies completely avoid high-risk projects? Explain.
A piece of equipment originally cost 80,000. It is expected to be used for five years and then sold for 800. Show your calculations of the amount of depreciation each year using (a) the reducing...
Have there been any studies that question the validity of the CAPM? Explain.
What do you think the average investors risk perception is now? In what types of investments do you think the average investor is investing currently?
Consider the matrix elements of L between two definite-parity states: (n''m'|L|nm). Under what conditions is this matrix element guaranteed to vanish? Note that the same selection rule would apply to...
Determine the center and radius of each circle. Sketch each circle. 4x 2 + 4y 2 9 = 16y
Use the given graph of f(x) = 1/x to find a number such that |x - 2| <8 0.5 < 0.2 whenever y4 1+ 0.7 0.5 0.3 10 10 2
Use the given graph of f to find a number δ such that 0
Use the given graph of f(x) = √x to find a number δ such that |√x 2| y=V 2.4 2- 1.6 ? ?
Factory overhead of $44,700 consists of Indirect labor of $21,900, Depreciation expense-Factory of $16,900, and Factory utilities of $5,900. a. Compute total manufacturing costs. b. Prepare a...
In Giannakakos et al. (2016), titled Using Video Modeling with voiceover Instruction plus feedback to train staff to implement direct teaching procedures, why do you think collecting data on the...
Presidio, Inc., produces one model of mountain bike. Partial information for the company follows: Required: 1. Complete Presidios cost data table. 2. Calculate Presidios contribution margin ratio and...

Show that if { (, (1, . . . , (n} is an orthogonal set of functions

Question:

Step by Step Answer:

If for all a ...View the full answer

Numerical Analysis

Students also viewed these Numerical Analysis questions