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,...
Dodger Corporation has been in the manufacturing business in the United States for more than 100 years. A tax consultant has proposed that Dodger use a corporate inversion to nominally move its...
The standard angle of a V-belt is (a) 30 (b) 35 (c) 40 (d) 45
Using the data from Exercises 3-1 and 3-2, prepare financial statements for May, including income statement, retained earnings statement, balance sheet, and statement of cash flows.
Losing to a Weaker Foe What began as a heavily conventional military campaign to unseat the regime of Saddam Hussein had become a bitter, unconventional struggle against frustrated Sunnis who...
Determine the resultant force acting on the 0.7-m-high and 0.7-m-wide triangular gate shown in Fig. P11??15 and its line of action. 0.3 m. 0.7 m 0.9 m Water 0.7 m
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...
Thembi is a trader. She maintains a full set of accounting records and posts the totals of the sales, purchases and returns journals to the ledger each month. On 1 March 201 the balances in her...
Can we apply binary search algorithm to a sorted linked list, why?
What is your default pattern when faced with conflict?
Suppose the numbers 0, 1, 2,. . . , 9 were pushed onto a stack in that order but that pops to occur at random points between the various pushes. The following is a valid sequence in which the values...
Name a time a disagreement almost ruined a relationship. a. What could you have done differently? b. How will you handle similar disagreements in the future?
What is the difference between a stack and an array?
(a) Draw mechanisms to account for the following two transformations, each of which leads to the same product. (b) Why are these new products favored over the starting materials under these...
Suppose that a flow network G = (V, E) violates the assumption that the network contains a path s t for all vertices V. Let u be a vertex for which there is no path s u t. Show that there must...
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.
ABC Hospital is one of two hospitals in the community. The Hospital offers all major specialty services (e.g. cardiology, neurology, pulmonology, etc.) The Hospital is approached by a cardiologist...
You obtained job-related information about the HR assistant position from O*Net. Answer the following sections based on that information. QUESTIONS: The following is the list of questions included in...
On January 8, the end of the first weekly pay period of the year, Regis Company's employees earned $27,760 of office salaries and $70,840 of sales salaries. Withholdings from the employees' salaries...

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