Let g1, g, . . . , gm be linear functionals on a linear space X. For

Question:

Let g1, g, . . . , gm be linear functionals on a linear space X. For fixed numbers cj, the systems of equations
gj(x) = cj, j = 1, 2, . . . ,m
is consistent if and only if

for every set of numbers Î»1, Î»2, . . . , Î»m.

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

Step by Step Answer:

Related Book For book-img-for-question

Foundations of Mathematical Economics

ISBN: 978-0262531924

1st edition

Authors: Michael Carter

See More Books

Question Posted: May 02, 2016 11:44 AM

See More Questions

Let (Y 1 , W 1 ), . . . , (Y n , W n ) be an i.i.d. sample of random vectors with finite covariance matrix Let Y and W be the sample averages. Let g(y, w) be a function with continuous partial...
Let f, g1, g2, ..., gm be linear functionals on a linear space X. f is linearly dependent on g1, g2, ..., gm, that is, f lin g1, g2, ..., gm if and only if kernel gj S kernel f
(a) Let G = (V, E) be a loop-free undirected graph, where |V| = 6 and deg(v) = 2 for all v V, Up to isomorphism how many such graphs G are there? (b) Answer part (a) for | V| -7. (c) Let G1 = (V1,...
Which of the following is most likely to be recognized as a defining characteristic of the public good? a) The good is a non-rival element. B) the good is a non-excludable item C) The good is both A...
Study the Excel regression output that follows. How many predictors are there? What is the equation of the regression model? Using the key statistics discussed in this chapter, discuss the strength...
For Further Research (Individual): One problem that traditional retailers face when they open online stores is cannibalization. Select a traditional retailer where you and your fellow students might...
Explicar por qu ciertos tipos de productos y servicios son muy convenientes para el marketing interactivo .
You collect data on 26 metropolitan areas to analyze average monthly debt payments in terms of income and the unemployment rate. A portion of the data is shown in the accompanying table. a. Estimate...
Indicate the effect that each of the following transactions has on the cash balance. Payment of cash dividends Increase cash Payment of interest Decrease cash Sale of treasury stock No change in cash...
Yoshi Company completed the following transactions and events involving its delivery trucks. Year 1 1 Paid $23,515 cash plus $1,785 in sales tax for a new delivery truck estimated to have a five-year...
Show the converse; that is, if f (x) = then f .(x). 0 for every x S where S . {x X : gj(x) = 0 = j . 1; 2 . . .m}. igiX
Let K be a closed convex cone in a finite-dimensional linear space X and M a subspace with K M = {0}. Then there exists a linear functional f X* such that f(x) > 0 for every x K\{0} and f(x) = 0...
Python eggs (1.1) How is the hatching of water python eggs influenced by the temperature of the snakes nest? Researchers assigned newly laid eggs to one of three temperatures: hot, neutral, or cold....
Discuss the Competitive Markets and Externalities simulations (both with and without policy interventions) . What impact do policy interventions have on the supply and demand equilibrium for a...
The best consultant to fix issue number one is Frederick Taylor who is credited with creating the scientific management movement (Lumen, n.d.). Since Taylor's work focused on how a process could be...
1. Which Pepsico products are growing faster than soft drinks (why) and by what percentage? 2. Why do the fastest growing products experience a more complex supply chain? Explain. 3. What are some of...
Use BLUF (Bottom Line UP Front) or Brief for answering the following questions: 1) There are a number of InfoSec frameworks / models available in industry. A. What is an InfoSec framework / model? B....
An introduction to organizational structure. Topics such as alternative organizational structures, the reciprocal relationship between multinational strategy and structure, and how recourses affect...
A series RL circuit, with R = 10 and L = 2 H, has an applied voltage v = 10 e 2 t cos (10t + 30).
The area of square PQRS is 100 ft2, and A, B, C, and D are the midpoints of the sides. Find the area of square ABCD. B A
A researcher claims that at least 10% of all football helmets have manufacturing flaws that could potentially cause injury to the wearer. A sample of 200 helmets revealed that 16 helmets contained...
A random sample of 500 registered voters in Phoenix is asked if they favor the use of oxygenated fuels year-round to reduce air pollution. If more than 315 voters respond positively, we will conclude...
The advertised claim for batteries for cell phones is set at 48 operating hours, with proper charging procedures. A study of 5000 batteries is carried out and 15 stop operating prior to 48 hours. Do...
Given the following financial data for the Smith Corporation, calculate the length of the firm's operating cycle (OC). Sales $2,610,000 Cost of Good Sold $2,088,000 Inventory $ 278,400 Accounts...
The predetermined overhead rate is usually calculated Group of answer choices At the end of each year At the beginning of each month At the beginning of the year At the end of the month
ajax county collects property taxes for the cities within the county, Ajax county collected 1000 from citizens in Beatty city that belong to Beatty city what would be the appropriate entries for ajax...

Let g1, g, . . . , gm be linear functionals on a linear space X. For

Question:

E9 = 0 =jej = 0 Σλο

Step by Step Answer:

The set 1 2 is a closed subspace in If the system is inconsistent c 1 ...View the full answer

Foundations of Mathematical Economics

Students also viewed these Numerical Analysis questions