If a1, a2,..., ak are nonzero scalars, show that span {a1X1, a2X2,..., akXk} = span{X1 ,X2,...,Xk) for

Question:

If a1, a2,..., ak are nonzero scalars, show that span {a1X1, a2X2,..., akXk} = span{X1 ,X2,...,Xk) for any vectors X, in Rn.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra With Applications

ISBN: 9780070985100

7th Edition

Authors: W. Keith Nicholson

See More Books

Question Posted: Jun 21, 2016 06:38 AM

See More Questions

In this exercise we derive an estimate of the average-case complexity of the variant of the bubble sort algorithm that terminates once a pass has been made with no interchanges. Let X be the random...
If a0 + a1 + a2 + . . . ak = 0 show that If you dont see how to probe this, try the problem-solving strategy of using analogy (see page 80). Try the special cases k = 1 and k = 2 first. If you can...
Show that the postulates of probability are satisfied by conditional probabilities. In other words, show that if P(B) 0, then (a) P(A| B) 0; (b) P(B| B) = 1; (c) P(A1 A2 .. . | B) = P(A1| B) +...
Marc & Kent operate a vineyard as partners. The partnership trades under the business name Victor Estate. Victor Estate has prepared a general ledger for the 2023 income year showing the following...
The following general ledger accounts are included in the trial balance for an audit client, Jones Wholesale Stationery Store. Accounts payable Insurance expense Accounts receivable Interest expense...
55. In July of this year, Stephen started a proprietorship called ECR (which stands for electric car repair). ECR uses the cash method of accounting and Stephen has produced the following financial...
What should Burton do about the ethical and legal problems facing Zales? LO.1
Orange Corp., a high-technology company, utilizes the following procedures for recording materials and transferring them to work in process. (1) Upon receipt of raw materials by stores, the...
ow.com/ilm/take Assignment/take Assignment Main do Pinprogress true eBook Multiple-step income statement and balance sheet The following selected accounts and their current balances appear in the...
Consider the following two mutually exclusive projects. Whichever project you choose, if any, you require a 15 percent return on your investment. a. If you apply the payback criterion, which...
In each case determine whether U is a subspace of R3. Support your answer. (a) U = {[1 s t]T | s and t in R}. (b) U = {[0 s t]T | s and t in R}. (c) U = {[r s t]T | r, s, and t in R, - r + 3s + 2t =...
Suppose that U = span {X1, X2,Xk} where each Xi is in Rn. If A is an m n matrix and AXi = 0 for each i, show that AY=0 for every vector Y in U.
1. Can a company gain advantages besides profit by offshoring? If so, what are they? If not, why not? 2. Does a company face ethical considerations in deciding whether to offshore activities? Why or...
7. This is a question about electromagnetic waves. (a) Starting from Maxwell's equations in a vacuum show that the electric field E and magnetic field B obey wave equations and identify the velocity...
Participate in workplace health and safety Third- party report Task 1: Case scenario: Workplace hazard collection and risk control form You are required to review this workplace inspection form and...
The red curve is the position-time x-t graph for the ladybug. Each tick mark on the time axis of the graph marks off 0.5 s. Note: you can hit reset graph and graph again to watch the graph form again...
Oma's Bakery is thinking about replacing the convection oven with a new, more energy-efficient model. Information related to the old and new ovens follows: (Click the icon to view the information...
One could argue that substantial travel for work is an undesirable characteristic of any job. What would the theory of compensating differentials predict about the relative wages of a sales position...
The three following reactions are acidbase reactions according to the Lewis theory. Draw Lewis structures, and identify the Lewis acid and Lewis base in each reaction. (a) B(OH)3 + OH (b) NH4 + H3O+...
The Place-Plus real estate development firm in Problem 24 is dissatisfied with the economists estimate of the probabilities of future interest rate movement, so it is considering having a financial...
Show that if {v1, v2} is linearly independent and V3 does not he in span (v1, v2}, then {v1, v2, v3} is linearly independent.
Use the Wronskian to show that the following sets of vectors are linearly independent. (a) 1, x, ex (b) sin x, cos x, x sin x
Which of the following sets of vectors in R4 are linearly dependent? (a) (3, 8, 7, -3), (1, 5, 3, -1), (2, -1, 2, 6), (1, 4, 0, 3) (b) (0, 0, 2, 2), (3, 3, 0, 0), (1, 1, 0, -1)
How do warehouses and distribution centers differ? What is cross-docking and why might a company choose to cross-dock a product? What kinds of products can be delivered electronically? What kinds...
Strawberry Inc. has historically been an all-equity firm. The analyst expects EBIT to be $1.5B in perpetuity starting one year from now. The cost of equity for the company is 11.5% and the tax rate...
Guzman company received a 60- day, 5 % note for 54,000 dated July 12 from a customer on account. Determine the due date on note. Determine the maturity value of the note and journalize the entry of...

If a1, a2,..., ak are nonzero scalars, show that span {a1X1, a2X2,..., akXk} = span{X1 ,X2,...,Xk) for

Question:

Step by Step Answer:

Since a i x i is in span x i for each ...View the full answer

Linear Algebra With Applications

Students also viewed these Linear Algebra questions