Consider the vector space C[-1, 1] with inner product defined by (a) Show that form an orthonormal

Question:

Consider the vector space C[-1, 1] with inner product defined by

(a) Show that

form an orthonormal set of vectors.
(b) Use the result from part (a) to find the best least squares approximation to h(x) = x1/3 + x2/3 by a linear function.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books

Question Posted: Jun 13, 2016 12:55 AM

See More Questions

Consider the vector space of continuous real-valued functions on [0, ] with an inner product defined by (f, g) = 0 f(t)g (t)dt. Show that the collection of functions sin nt, for n = 1, 2.... is an...
Consider the functions f(x) = 1 and g(x) = x - 3/4 as elements of the vector space C[0, 1]. For each of the indicated norms, compute ||f||, ||g||, ||f + g||. and verify the triangle inequality: (a)...
Let V - P(1) be the vector space consisting of linear polynomials p(t) = at + b. (a) Carefully explain why defines an inner product on V. (b) Find all polynomials p(t) = a t + b V that are orthogonal...
Helium gas is throttled steadily from 500 kPa and 70C. Heat is lost from the helium in the amount of 2.5 kJ/kg to the surroundings at 25C and 100 kPa. If the entropy of the helium increases by 0.25...
You own a $1,000-par zero-coupon bond that has five years of remaining maturity. You plan on selling the bond in one year, and believe that the required yield next year will have the following...
Required query (textbook pg 105-115, modified): (1)For which items are there at least 5 units in quantity on hand? (2)List the invoice number, dates, and salesperson for sales made to Rodney Wern....
Support for the form of the generalized version of Fick's law introduced in this chapter can be found in the thermodynamics of irreversible processes. Here we introduce a brief description of this...
What macroenvironmental factors have affected Targets performance during that period? When you hear the term discount retail, two names that usually come to mind: Walmart and Target. The two have...
The CDS curve in question is shown: Table 1: CDS Curve CDS Maturity (Years) 1234567 Quoted Flat CDS Spread (bp) 30 40 50 60 70 80 90 8 100 9 110 10 120 The CDS spreads shown in this table are Quoted...
Mr B aged 52 years, has earned rupees 75,00,000 out of his business. His ex-wife gifted him a car worth rupees 8 lakh. He spent a total of rupees 20 lakh during a family trip. He won a lottery of 16...
The functions cos x and sin x are both unit vectors in C[-Ï, Ï] with inner product defined by (a) Show that cos x ¥ sin x. (b) Determine the value of ||cos x + sin x||2. = | f(x)g(x)dx
Let v1 and v2 be vectors in an inner product space V. (a) Is it possible for | < v1, v2 > I > ||v1|| ||v2|| Explain. (b) If | < vl, v2 > | = ||v1|| ||v2|| what can you conclude about the vectors v1...
Consider the closed loop system of Problem 5.4. Knowing the input, output, and feedback path transfer function, identify the system using (a) the "deconvolution" matrix and (b) the recursive approach...
Multiply. (510-4)(1-25) Simplify your answer as much as possible.
An American firm owes A$1,500,000.00 payable in one year. The current spot it$1.7500/A$. An Australian bank is paying 4.50% on deposits or will lend at 7.50%. A U.S. bank is paying 2.50% or will lend...
You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms. Find how much the account needs to hold to make this possible. Round your answer to the...
You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms. Find how much the account needs to hold to make this possible. Round your answer to the...
On her first day at the helm of the nearly 160-year-old Belgian chemical company, Ms. Kadri says, she started to work on a 10-year sustainability road map for the firm that was unveiled earlier this...
In Problem refer to the Venn diagram below and find the indicated number of elements. n(A B) U A B 21 42 18 19
(a) Use integration by parts to show that (b) If f and g are inverse functions and f' is continuous, prove that (c) In the case where f and t are positive functions and b > a > 0, draw a diagram to...
Determine whether and are parallel in each of the following cases. (a) = [3 -6 3]T; = [-1 2 -1]T (b) = [2 0 -1]T; = [-8 0 4]T
Let and be the position vectors of points P and Q, respectively, and let R be the point whose position vector is + . Express the following in terms of and . (a) (b) where O is the origin RO
In each case, find (a) P(2, 0, 1), Q(1, -1, 6) (b) P(1, -1, 2), Q(1, -1, 2) (c) P(3, -1, 6), Q(1, 1, 4) PO and PO.
Prove that Russian multiplication does what it needs to do, i.e. the result is the product of the two integers. Do not use the proof of the book. It is mainly an exercise in understanding the binary...
What is the fundament difference between growing a unicorn versus a camel? What are the financial recommendations for start-ups and the reasons given for those choices? Do you agree with these...
16. Nickel Inc. bought $500,000 of 3-year, 9% bonds as an investment on December 31, 2015 for $545,000. Nickel uses straight-line amortization. On May 1, 2016, $100,000 of the bonds were redeemed at...

Consider the vector space C[-1, 1] with inner product defined by (a) Show that form an orthonormal

Question:

/6 and 112(x)= 11 i (x)=→

Step by Step Answer:

a u 1 x u 2 x 1 1 12 62 xdx 0 u 1 x u 1 x 1 1 ...View the full answer

Linear Algebra with Applications

Students also viewed these Linear Algebra questions