Let W be a nonempty subset of a vector space V. Prove that W is a subspace

Question:

Let W be a nonempty subset of a vector space V. Prove that W is a subspace of V if and only if ru + sv is in W for any vectors u and v in W and any scalars r and s.

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 07:03 AM

See More Questions

Let U be a nonempty subset of a vector space V. Show that U is a subspace of V if and only if u1 + au2 lies in U for all u1 and u2 in U and all a in R.
Let S be a nonempty subset of a linear space, and let m = dim S = dim aff S. Suppose that x belongs to conv S so that there exist x1, x2, . . . , xn S and a1, a2, . . . , an R+ with a1,......,...
Let S be a nonempty subset of a linear space and let m dim cone S. For every x cone S, there exist x1,x2,...,xn S and Î±1, Î±2, . . ., Î±n + Such that x =...
Differentiate implicitly to find 2x + 5xy + 5y +16y - 8 = 0; dy dx . Then find the slope of the curve at the given point. (-2,0)
Clampett Oil purchases crude oil products from suppliers in Texas (TX), Oklahoma (OK), Pennsylvania (PA), and Alabama (AL), from which it refines four end-products: gasoline, kerosene, heating oil,...
LO4 George purchases stock in Dodo Corporation in 2006 at a cost of $50,000. In 2010, he sells the stock for $32,000. What is the effect of the sale of stock on Georges taxable income? Assume that...
5. Which of the following statements characterizes a consolidated entity? a It has an independent management board b It operates solely out of its headquarters c It does not exist d None of the above
Spearman Domestic Equity Fund sells two types of share, A+ and B+. A+ shares are sold with frontend load fee of 6% whilst Type B+ shares are not subject front-end load fee but are charged to...
Prices of securities that are traded on the organized exchanges are determined by a. a "bid" and "ask" negotiation process amongst brokers who hold these securities in their own account. b. the...
What was Spangler's mistake?
Prove that a subspace W of R3 coincides with R3 if and only if it contains the vectors And 001
Let V be the set of all polynomials of (exactly) degree 2 with the definitions of addition and scalar multiplication as in Example 6. (a) Show that V is not closed under addition. (b) Is V closed...
Match each of the given differential equations with one or more of these solutions: (a) y = 0, (b) y = 2, (c) y = 2x, (d) y = 2x 2 . 1. xy' = 2y 2. y' = 2 3. y' = 2y 4 4. xy' = y 5. y'' + 9y = 18 6....
226 Payroll Accounting Chapter 7: Comprehensive Projects-Paper-Based Versions One-Month Project NOTE! Templates needed to complete these exercises, including one containing year-to-date payroll data,...
The Westchester Chamber of Commerce periodically sponsors public service seminars and programs Currently, promotional plans ore under way for this year's program Advertising alternatives include...
Mastery Problem: Activity-Based Costing WoolCorp WoolCorp buys sheep's wool from farmers. The company began operations in January of this year, and is making decisions on product offerings, pricing,...
The following system of linear equations is called underdetermined because there are more variables than equations. x2x 3x3 = 4 2x1x2 + 4x3 = -3 Similarly, the following system is overdetermined...
Write a 2000-word Reflection paper on " Country Managers Simulation by considering the following points: Countries chosen during the simulation were Argentina and Brazil: 1. Explain why you did what...
(a) Find the voltage near a 10.0 cm diameter metal sphere that has 8.00 C of excess positive charge on it. (b) What is unreasonable about this result? (c) Which assumptions are responsible?
Perform the operation by first converting the numerator and denominator to scientific notation. Write the answer in scientific notation. 7,200,00/0.000009
Find the Euclidean norm of v if (a) v = (1, i) (b) v = (2i, 0, 2i + 1, - 1)
Find the Euclidean inner product u v if. (a) u = ( - i 3i), v = (3i, 2i) (b) u = (3 - 4z, 2 + i, - 6i),v = (1 + i, 2 - i, 4)
Let u = (u1, u2) and v = (v1, v2). Show that (u, v) = 3u1I + 2u22 defines an inner product on C2.
QUESTION 3 A business owns seven flats rented out to staff at R500 per month. All flats were tenanted Ist january 21 months rent was in arrears and as at 31st December 14 months' rent wa Identify the...
1. 2. 3. Select the Tables sheet, select cells A6:B10, and create range names using the Create from Selection button [Formulas tab, Defined Names group]. Select cells B1:F2 and click the Name box....
Tropical Rainwear issues 3,000 shares of its $18 par value preferred stock for cash at $20 per share. Record the issuance of the preferred shares. (If no entry is required for a particular...

Let W be a nonempty subset of a vector space V. Prove that W is a subspace

Question:

Step by Step Answer:

Suppose that W is a subspace of V Let u and v be in W and ...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions