Let S = {v1, . . . , vn} be a spanning set for a vector space

Question:

Let S = {v1, . . . , vn} be a spanning set for a vector space V. Show that if vn is in span (v1, . . . , vn-1), then S' = {v1, . . . , vn-1} is still a spanning set for 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 A Modern Introduction

ISBN: 978-1285463247

4th edition

Authors: David Poole

See More Books

Question Posted: Apr 15, 2016 06:27 AM

See More Questions

Let S = {v1, . . . , vn} be a linearly independent set in a vector space V. Show that if v is a vector in V that is not in span(S), then S' = {v1, . . . , vn, v} is still linearly independent.
Let S = {v1, . . . , vn} be a set of vectors in a vector space V with the property that every vector in V can be written as a linear combination of v1, . . . , vn in exactly one way. Prove that S is...
Let S = {v1, v2, ( v"} be an ordered basis for an n-dimensional vector space V. Show that is an ordered basis for Rn. V2 {[v]s[v]s[v.J
Do the following problems mentally using the distributive property. a. 5 99 b. 4 88 c. 8 52
The following information is taken from Oler Corp.s balance sheet at December 31, 2013. Interest is payable annually on January 1. The bonds are callable on any annual interest date. Oler uses...
The plant manager of Shannon Electronics Company is considering the purchase of new automated assembly equipment. The new equipment will cost $2,400,000. The manager believes that the new investment...
The University of Wisconsin at Madison completed a study titled GenderEquity Study of Faculty Pay,dated June 5, 1992. The main purpose of the study was to determine whether women are treated unfairly...
A psychologist compares the mean amount of time of rapid-eye movement (REM) sleep for subjects under three conditions. She randomly assigns 12 subjects to the three groups, four per group. The sample...
Andrew Ghez is the new chief financial officer ( CFO ) for Millcreek Company. Andrew has a long career as a financial accountant. In his new role as CFO, he will be supervising the work of both the...
As someone who came of age in the "post email" world of blogs, wikis, social networks, and other Web 2.0 technologies, you were rather disappointed to find your new employer solidly stuck in the age...
Find a basis for span(sin2x, cos2x, cos 2x) in P.
Let {v1, . . . , vn} be a basis for a vector space V and let c1, . . . , cn be nonzero scalars. Prove that {c1v1, . . . , cnvn} is also a basis for V.
In a two-way ANOVA experiment, factor A is operating on 3 levels, factor B is operating on 2 levels, and there are 2 replications per cell. If MSAyMSE = 5.35, MSByMSE = 5.72, and MSAByMSE = 6.75, and...
Study the organizational chart in figure 3.5. What kinds of day-to-day activities would you expect to take place for the employees in each box? How would you expect them to share information across...
What role do focus and reflection play in workplace learning and problem solving?
For each number $x$ in the domain, the corresponding range value $y$ is found by taking the square root of the domain value subtracted from 5.
What types of ethical principles are embedded in the student code of conduct at your university? Should these be followed to the same degree in all student situations? Why or why not?
Think about recent graduates of your technical communication program. Where are they employed? What courses and minors did they take with their degrees? Were these courses and minors beneficial to...
If the current financial reporting of transactions is well understood by users it is confusing to require a change when none is sought by the users. Discuss.
What is the maximum volume of 0.25 M sodium hypochlorite solution (NaOCl, laundry bleach) that can be prepared by dilution of 1.00 L of 0.80 M NaOCl?
the given matrix is of the form In each case, A can be factored as the product of a scaling matrix and a rotation matrix. Find the scaling factor r and the angle of rotation. Sketch the first four...
the given matrix is of the form In each case, A can be factored as the product of a scaling matrix and a rotation matrix. Find the scaling factor r and the angle of rotation. Sketch the first four...
the given matrix is of the form In each case, A can be factored as the product of a scaling matrix and a rotation matrix. Find the scaling factor r and the angle of rotation. Sketch the first four...
a) Solve cos x = 2xy and cos xy = 2x to 5 decimal places with an initial guess of x0 = 0.5 and yo= 0.5 using proper method. (90 Point) ATTENTION: Please add a comment line to each line of code...
Write a program that will asks the user to input 15 students test score then store them in an array named "Score" your program should accomplish the followings: 1. Calculate and display the average....
4. What is clock synchronization? Synchronize the network given below when the server. advances 10 second using Berkeley algorithm. Server 2:35 2:00 2:20 1:55 Client 1 Client 2 Client 3

Let S = {v1, . . . , vn} be a spanning set for a vector space

Question:

Step by Step Answer:

If v n spanv 1 v n1 then there are constants such that v n c 1 ...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Linear Algebra questions