If S v 1 , ,v k is an affinely independent subset of R n prove that k n 1 ...

If k n 1 then k1n and the k1 vectors in v2 V Vk ...

If S = {v 1 ,.........,v k } is an affinely independent subset of R n ;

Question:

If S = {v₁,.........,v_k} is an affinely independent subset of Rⁿ; prove that k ≤ n + 1.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra And Its Applications

ISBN: 9781292351216

6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

See More Books

Question Posted: May 17, 2023 08:55 AM

See More Questions

Show that any linearly independent subset of Rn can be orthogonalized without changing its span.
Suppose that {p 1, p 2, p 3 } is an affinely independent set in R n and q is an arbitrary point in R n . Show that the translated set {p 1 + q, p 2 + q, p 3 + q} is also affinely independent.
Mark each statement True or False (T/F). Justify each answer. If S = {v 1 ,...,v p ) is an affinely independent set in R n and if p in R n has a negative barycentric coordinate determined by S, then...
Use (4.1), for a perfectly conducting fluid, and the nonlinear equation of continuity (1.1), to show that the change of B with time in a fluid element is related to changes of density according to...
In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it is about 50% lighter than the standard iPad. Battery tests for the...
Prince Observation incorporated on May 1, 2024, and was authorized to issue 500,000 common shares and 100,000 5%, non-participating, convertible preferred shares. During the remainder of 2024, the...
You are provided with the cost of goods manufactured statement and income statement for International Manufacturers Pty Ltd. Required Prepare the closing entries for International Manufacturers Pty...
Robert and Stanley held legal title of record to adjacent tracts of land, each consisting of a number of five acres. Stanley fenced his five acres in 1986, placing his east fence fifteen feet onto...
What critical assumptions has TESLA made to value inventory? Does TESLA use FIFO or LIFO? Explain what is LCM (the lower of cost or market) and how this may impact inventory every year. Cost of...
Mark each statement. Justify each answer. (T/F) A linear transformation from R to R n is called a linear functional.
Mark each statement True or False (T/F). Justify each answer. The 4-dimensional simplex S 4 has exactly five facets, each of which is a 3-dimensional tetrahedron.
Explain briefly how to use the physical units, relative sales value net realisable and constant gross margin methods of joint cost allocation. Which method is the best?
A $10 \%$ rich mixture of heptane $\left(\mathrm{C}_{7} \mathrm{H}_{16} ight)$ and air is trapped in the cylinder of an engine at a pressure of $1 \mathrm{bar}$ and temperature of \(400...
A turbocharged, intercooled compression ignition engine is operated on octane $\left(\mathrm{C}_{8} \mathrm{H}_{18} ight)$ and achieves constant pressure combustion. The volumetric compression...
Revisit the guidelines in this chapter for negotiating a job offer. Then, with the two classmates you worked with for Exercise 16, practice negotiating. Divide roles: the hiring manager, candidate,...
An engine runs on a rich mixture of methyl and ethyl alcohol and air. At a pressure of 1 bar and $10^{\circ} \mathrm{C}$ the fuel is completely vapourised. Calculate the air-fuel ratio by volume...
A gas engine with a volumetric compression ratio of $10: 1$ is run on a weak mixture of methane $\left(\mathrm{CH}_{4} ight)$ and air, with $\phi=0.9$. If the initial temperature and pressure...
What does it mean to say that economists use the scientific method? How do economists distinguish between models that work and those that dont?
What are three disadvantages of using the direct write-off method?
An article in Advanced Semiconductor Manufacturing Conference (ASMC) (May 2004, pp. 32529) stated that dispatching rules and rework strategies are two major operational elements that impact...
Consider the earth-moving experiment in Exercise 14-34. The experiment actually used two different operators with the production in columns 1 and 3 from operator 1 and 2, respectively. Analyze the...
An article in Journal of Hazardous Materials [Biosorption of Reactive Dye Using Acid-Treated Rice Husk: Factorial Design Analysis (2007, Vol. 142(1), pp. 397403)] described an experiment using...
You quit your job where you earned a year to start your own widget business. To start your business, you cashed in your investments of which earned you a year in interest. In the first year, you sold...
The following information is provided for a company. Accounts payable Buildings Cash $36,000 $192,000 $25,200 Accounts receivable $22,800 Salaries payable $10,800 Retained earnings $114,000 Supplies...
Company A has the following information applicable to its products: Total Overheads = 100,000 Total machine Hours = 50,000 Product A B Units of Production 2,500 5,000 Material Cost p/unit Labour Cost...

If S = {v 1 ,.........,v k } is an affinely independent subset of R n ;

Question:

Step by Step Answer:

If k n 1 then k1n and the k1 vectors in v2 V Vk ...View the full answer

Linear Algebra And Its Applications

Students also viewed these Mathematics questions