Show that if W is a subspace of a finite-dimensional vector space V, then W is finite-dimensional

Question:

Show that if W is a subspace of a finite-dimensional vector space V, then W is finite-dimensional and dim W ( dim V.

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

Step by Step Answer:

Related Book For book-img-for-question

Elementary Linear Algebra with Applications

ISBN: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

See More Books

Question Posted: Jun 21, 2016 07:04 AM

See More Questions

Show that if W is a subspace of an inner product space V that is spanned by a set of vectors S, then a vector u in V belongs to W if and only if u is orthougonal to every vector in S.
Let U be a subspace of a finite dimensional vector space V. (a) Show that U = ker T for some linear transformation T: V V. (b) Show that U = im S for some linear transformation S: V V.
Show that if W1 W2 are finite dimensional subspaces of an inner product space, then W1 W2.
If a large chilled water plant has 6 chillers and 5 of them are operating at 1 0 0 % , when the operator starts the 6 th chiller, to what percent do the first 5 chillers unload? What formula do you...
A residential moving company needs to move a family from city 1 to city 12 in Figure where the numbers on the arcs represents the driving distance in miles between cities. a. Create a spreadsheet...
Describe some of the important practices and procedures designed to improve service to customers in the following areas: ramp, ground personnel, aircraft, and flight personnel. LO1
E2-10 Calculate income and investment balance for midyear investment Pam Corporation acquired 25 percent of Sun Corporations outstanding common stock on October 1, for $300,000. A summary of Suns...
The 2011 balance sheet of Annas Tennis Shop, Inc., showed $490,000 in the common stock account and $3.4 million in the additional paid-in surplus account. The 2012 balance sheet showed $525,000 and...
Book Assets Current assets: Cash Accounts receivable (net) Notes receivable Inventory Prepaid expenses Total current assets Equipment (net) Liabilities and Equity Current liabilities: $ 63 Accounts...
Match the continuous auditing alarms to flag the fraud schemes. Fraud Scheme a. Operating expenses were illegitimately reclassified as capital expenditures, which improved the expenditure-to-revenue...
Prove that the vector space P of all polynomials is not finite-dimensional. Suppose that {p1(t), p2(t), ( ( ( ( Pk(t)} is a finite basis for P. Let dj = degree Pj (t). Establish a contradiction.
Show that if W is a subspace of a finite-dimensional vector space V and dim W = dim V, then W = V.
Practice drawing a chair several times using a blank piece of paper. Repeat the procedure until you can do it without looking at the instructions above. For each of your chairs, make sure that it...
What makes a set of objects a vector space? You will no doubt want to refer to notes and the text, but I'd like you to summarize it for starters. If you have identified a vector space, for example...
Walla Walla Company is in its planning stage for next year. Walla Walla expects a big Quarter 3 and is creating a production budget to determine if it needs to hire more employees. Walla Walla knows...
Task: P9 P9a P9b P9c P9d Describe the principles and applications of electromagnetic induction Describe using a series of bullet point statements, how transformers work and how their operation...
Based on the given information, analyse company's financial health and provide future projections. Unit FY16 FY17 FY18 FY19 Sales Rs. Cr 134 245 371 1,159 PAT Rs. Cr (281) (585) (78) (571) Assets Rs....
OBJECTIVE QUESTIONS 1. In each of the following only one statement/item is correct. State which. (i) Financial Accounting helps in (a) ascertaining the financial position of the concerned firm, (b)...
What is the capacitance of a large Van de Graaff generators terminal, given that it stores 8.00 mC of charge at a voltage of 12.0 MV?
Nike manufactures shoes and sportswear. How has the Internet changed the way this company communicates with its suppliers and retail customers?
Juliet has a choice between receiving a monthly salary of $1800 from Furniture by Design or a base salary of $1600 and a 4% commission on the amount of furniture she sells during the month. For what...
Soledad worked 48 hr one week and earned a $442 paycheck. She earns time and a half (1.5 times her regular hourly wage) for the number of hours she works in excess of 40. What is Soledad's regular...
City Cabs charges a $1.75 pickup fee and $1.50 per mile traveled. Diego's fare for a cross-town cab ride is $19.75. How far did he travel in the cab?
*Prepare the plant assets section of Amphonie's balance sheet at December 31, 2021 using the information below. At December 31, 2020, Amphonie Company reported the following as plant assets. Land $...
Question 1 of 1 - / 100 View Policies Current Attempt in Progress Pargo Company is preparing its budgeted income statement for 2020. Relevant data pertaining to its sales, production, and direct...
Schopp Corporation makes a mechanical stuffed alligator that sings the Martian national anthem. The following information is available for Schopp Corporation's anticipated annual volume of 500,000...

Show that if W is a subspace of a finite-dimensional vector space V, then W is finite-dimensional

Question:

Step by Step Answer:

Let dim V n First observe that any set of vectors in W that is linearly ...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions