(a) Prove that the set B = {p0 (x), p1 (x) , . . . , Pn(x)}...

Question:

(a) Prove that the set B = {p0 (x), p1 (x) , . . . , Pn(x)} of Lagrange polynomials is linearly independent in Pn.
(b) Deduce that B is a basis for Pn.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra A Modern Introduction

ISBN: 978-1285463247

4th edition

Authors: David Poole

See More Books

Question Posted: Apr 15, 2016 06:27 AM

See More Questions

Determine if each set is linearly independent in the natural space. (a) (b) {(1 3 1), (-1 4 3), (-1 11 7)} (c) 0 120 04 0 0 2 1
Prove that each set {f, g} is linearly independent in the vector space of all functions from R+ to R. (a) f(x) = x and g(x) = 1/x (b) f(x) = cos(x) and g(x) = sin(x) (c) f(x) = ex and g(x) = ln(x)
Let a0, a1, . . . , an be n + 1 distinct real numbers. Define polynomials p0(x), p1 (x), . . . , Pn(x) by These are called the Lagrange polynomials associated with a0, a1, . . . , an [Joseph-Louis...
Let be an arbitrary operation in Problems 5259. Describe the operation for each problem. 5038; 70 2= 9; 901 = 10; 8 0 2 = 10; -
The following section is taken from Mareskas balance sheet at December 31, 2013. Current liabilities Interest payable ............. $ 40,000 Long-term liabilities Bonds payable (8%, due January 1,...
Explain the difference between the side offset and end offset options in geocoding.
2. How do the national cultures affect how the EDB functions?
What are typical maturities, denominations, and interest payments of a corporate bond? What mechanisms protect bondholders?
Suppose you have a liability policy with a $900,000 annual aggregate deductible. a. Calculate the losses paid by insurance when the annual loss is $2M and $500,000, respectively. (5 Marks) b. Draw...
Assume that you recently graduated with a major in finance and just landed a job in the trust department of a large regional bank. Your first assignment is to invest $100,000 from an estate for which...
Let {v1, . . . , vn}be a basis for a vector space V. Prove that {v1, v1 + v2, v1 + v2 + v3 , . . . , v1 + . . . + vn} is also a basis for V.
If q(x) is an arbitrary polynomial in Pn' it follows from Exercise 60(b) that q (x) = c0p0(x) + . . . + cnpn(x).....................(1) for some scalars c0, . . . , cn. (a) Show that ci = q (ai) for...
In the past, some governments have favored being selfsufficient and only import products that cannot be produced domestically. Do you believe that this is a sound economic policy? Explain.
3) A spider crawls with constant speed vo on a phonograph turntable rotating with constant angular speed w in the xy plane on a radially outward path, relative to the centre of the turntable. The...
Question Encik Zubir ( a certified handicapped person ) is the owner of a financial consulting firm, Bijak Wealth Enterprise. The business assists its clients to grow their wealth. Encik Zubir is...
What is XYZ Corp.'s net cash flow XYZ Corp. (for 2020) Revenue $5,000,000 Wages: $1,000,000 D&A: $1,000,000 Property, Plant & Equipment investment: $1,500,000 Tax Rate: 35% NOWC (2020): $750,000 NOWC...
Tower x (m) y (m) UU3 -118.1 -15.6 OU1 -85.3 -15.9 Sensor heights (m) 3.19, 4.16, 5.04, 7.24, 9.84 1.5, 3.0, 5.46, 9.86, 15.65 OU2 -90.0 -8.3 1.5, 2.96, 5.97, 9.91, 15.08 ASU -22.8 -8.6 5.0 UUT -13.3...
For each of the matrices determine the value(s) of c for which the given matrix is not invertible. [4 25. 26. 3 5 } ] 6 27. 28. 2 c+4 C -8 c-6]
What do you think computers will be like in the year 2020? Use the history from this chapter, along with your own experiences, to answer this question. Shopping in 2020 www
Consider the following cash flows in Table P5.5. (a) Calculate the payback period for each project. (b) Determine whether it is meaningful to calculate a payback period for project D. (c) Assuming...
If a square matrix A has two equal rows, why must A have 0 as one of its eigenvalues?
Show that l is an eigenvalue of A and find one eigenvector corresponding to this eigenvalue. = 4
The unit vectors x in R 2 and their images Ax under the action of a 2 Ã 2 matrix A are drawn head-totail, as in Figure 4.7. Estimate the eigenvectors and eigenvalues of A from each...
Cash from Operating Activities: ______________ Cash from Investing Activities: ______________ Cash from Financing Activities: ______________ Problem 2: Financial Ratios The GAP Macys 1 Current Ratio...
On January 1, 2021, Winky Enterprises issued 12% bonds dated January 1, 2021, with a face amount of $2,800,000. The bonds mature in 2030 (10 years). For bonds of similar risk and maturity, the market...
Using the following accounts and balances, prepare the stockholders' equity vection of the balance sheet. Pilty thousand shares of common stock are authorised, and 1,000 shares have been recoured,...

(a) Prove that the set B = {p0 (x), p1 (x) , . . . , Pn(x)}...

Question:

Step by Step Answer:

a Note first that the degree of each p i is n since there a...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Linear Algebra questions