Let v1, v2,...,vn be linearly independent vectors in a vector space V. Show that v2...., vn cannot

Question:

Let v1, v2,...,vn be linearly independent vectors in a vector space V. Show that v2...., vn cannot span V.

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: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books

Question Posted: Jun 13, 2016 12:50 AM

See More Questions

Let x1, x2,..., xk be linearly independent vectors in a vector space V. (a) If we add a vector xk+1 to the collection, will we still have a linearly independent collection of vectors? Explain. (b) If...
Let v1,... , vn and w1.......wn be two sets of linearly independent vectors in Rn. Show that all their dot products are the same, so vi vj = wi wj for all 1, 7 = 1........n, if and only if there is...
Let A be an n ( n matrix and {v1, v2, ( ( ( ( vk} a linearly dependent set of vector in Rn. Are Av1, Av2, ( ( ( ( Avk linearly dependent or linearly independent vectors in Rn? Justify your answer.
Mexico discovers huge reserves of oil and starts exporting oil to the United States. Describe how this would affect the following. a. The nominal pesoU.S. dollar exchange rate. b. Mexican exports to...
Huskie Motors just paid an annual dividend of $1.00 per share. Management has promised shareholders to increase dividends at a constant rate of 5%. If the required return is 12%, what is the current...
Identify the roles an effective manager must play.
Answer the problem on the basis of the given graph and the most likely estimates given as follows: Graph: If the profit (RE) is decreased by 5%, this project is not profitable. (a) True (b) False
Carla Hilton is a realtor. She organized the business as a corporation on December 16, 2013. The business received $55,000 cash from Hilton and issued common stock. Consider the following facts as of...
Swifty Corporation had the following transactions in debt instruments purchased to earn interest during the year ended December 31, 2021: Jan. 1 June 30 July 5 Oct. 1 Purchased a 180-day (six-month)...
Elena Bellisario began a new consulting firm on January 3. The accounting equation showed the follow- ing transactions. Analyze the equation and describe each of the transactions with their amounts....
Let {v1,..., vn} be a spanning set for the vector space V, and let v be any other vector in V. Show that v, v1, ..., vn are linearly dependent.
For each of the following, show that the given vectors are linearly independent in C[0, 1]. (a) cos x, sin x (b) x3/2, x5/2 (c) 1, ex + e-x, ex - e-x (d) ex, e-x, e2x
What role can HR and L&D practitioners play in engendering employee engagement as a means for improving organisational performance?
Your client who is currently using only Facebook and Instagram wants to try LinkedIn. What would you do first ? and why ?
Exro Technologies Corp. (Exro) is an upstart Canadian company that specializes in the manufacture of electric motors and batteries for electric bikes. Exro uses a job costing system and during...
How do neurobiological mechanisms, such as the stress response system and emotional regulation pathways, influence the dynamics of conflict escalation and resolution?
What is the consideration to invest in the company which has recorded revenue growth over the past 5 years but the Debt to Equity ratio also increase significantly to 5.72?
Builder Products, Incorporated, uses the weighted-average method in its process costing system. It manufactures a caulking compound that goes through three processing stages prior to completion....
Which system does more work: (a) E = 2436 J, q = 400 J; or (b) E = 317 J, q = 347 J?
A genetically engineered strain of Escherichia coli (E. coli) is used to synthesize human insulin for people suffering from type I diabetes mellitus. In the following simplified reaction scheme,...
Express the following as linear combinations of u = (1, 0, - i), v = (1 + i, 1, 1 - 2i), and w = (0, i, 2). (a) (1, 1, 1) (b) (0, 0, 0)
Determine which of the following lie in the space spanned by f = eix and g = e-ix (a) cos x (b) sin x (c) cos x + 3i sin x
Which of the following sets of vectors in C3 are linearly independent? (a) u1 = (1 - i, 1, 0), u2 = (2, 1 + i, 0), u3 = (1 + i, i, 0) (b) u1 = (z, 0, 2 - i), u2 = (0, 1, i), u3 = (- i, - 1 - 4i, 3)
Duncan Inc. issued 500, $1,200, 8%, 25 year bonds on January 1, 2020, at 102. Interest is payable on January 1. Duncan uses straight-line amortization for bond discounts or premiums. INSTRUCTIONS:...
WISE-HOLLAND CORPORATION On June 15, 2013, Marianne Wise and Dory Holland came to your office for an initial meeting. The primary purpose of the meeting was to discuss Wise-Holland Corporation's tax...
Stock in ABC has a beta of 0.9. The market risk premium is 8%, and T-bills are currently yielding 5%. The company's most recent dividend is $1.60 per share, and dividends are expected to grow at a 6%...

Let v1, v2,...,vn be linearly independent vectors in a vector space V. Show that v2...., vn cannot

Question:

Step by Step Answer:

If v 2 v n were a spanning set for V then we ...View the full answer

Linear Algebra with Applications

Students also viewed these Linear Algebra questions