(a) Show that any set of four vectors in R2 is linearly dependent. (b) Is this true...

Question:

(a) Show that any set of four vectors in R2 is linearly dependent.
(b) Is this true for any set of five? Any set of three?
(c) What is the most number of elements that a linearly independent subset of R2 can have?

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra

ISBN: 9780982406212

1st Edition

Authors: Jim Hefferon

See More Books

Question Posted: Jun 01, 2016 01:54 AM

See More Questions

Show that any set of five points from the plane R 2 lie on a common conic section, that is, they all satisfy some equation of the form ax 2 +by 2 +cxy+dx+ey+f = 0 where some of a, : : : , f are...
Is there a set of four vectors in R3 such that any three form a linearly independent set?
With a some calculation we can get formulas to determine whether or not a set of vectors is linearly independent. (a) Show that this subset of R2 is linearly independent if and only if ad - bc 6= 0....
Write a filter KamasutraCipher that takes two strings as command-line argument (the key strings), then reads strings (separated by whitespace) from standard input, substitutes for each letter as...
This chapter has assumed that labor is supplied by individual workers acting competitively. In some markets, however, the supply of labor is determined by a union of workers. a. Explain why the...
Nestles financial statements are presented in Appendix B. Financial statements of Zetar are presented in Appendix C. Instructions (a) At the end of the most recent fiscal year reported, what was...
Regional Hospital is a 500-bed hospital and several associated clinics in a major East Coast metropolitan area. It has been an aggressive adopter of computing technologies in efforts to decrease...
The following is the balance sheet of Korver Supply Company at December 31, 2010. The note payable is dated June 30, 2010 and is due on June 30, 2012. Interest at 6% is payable annually on June 30....
Net income for June\ Withdrawals by Billie Soares in June\ Additional investment by Billie Soares in June\ 115,000\ 25,000\ 50,000 \ a. Prepare a statement of owner's equity for the month ended June...
A long uniform rod of 50-mm diameter with a thermal conductivity of 15 W/m K is heated internally by volumetric energy generation of 20 kW/m 3 . The rod is positioned coaxially within a larger...
Prove that a polynomial gives rise to the zero function if and only if it is the zero polynomial. (Comment. This question is not a Linear Algebra matter but we often use the result. A polynomial...
In R4 what is the biggest linearly independent set you can find? The smallest? The biggest linearly dependent set? The smallest? ('Biggest' and 'smallest' mean that there are no supersets or subsets...
It was 5:30 Friday afternoon, January 22, 2016. Bill Hall, the chairman and CEO of National Brands Inc. was clearing up the last of the papers on his desk and was looking forward to a relaxing...
Since the Digital Millennium Copyright Act and other legislation and technology aimed at deterring digital pirating, it has become much more difficult and can carry hefty fines. Do you think...
Consider the seven-step strategy in decision-making. You are required to apply it to the problem of Special Operations Executive (SOE) & zones of special operation (ZOSO)in St. James Jamaica, school...
Is being a great manager the same as being a great leader? Why or Why not? Provide example of someone you have worked with who was a great leader and why did you think they were a great leader?
How do the main characters in Sharon Bala's book The Boat People develop a fighting spirit as a result of their desire to overcome obstacles in their path, notably the injustices they experience as...
Why is there an increase in the lambda_(max) (in nm) value of the compounds; CH_(4)(125),CH_(3)CH_(2)CH_(3) (135), Cyclopropane (190)?
For the following exercises, express each function H as a composition of two functions f and g where H(x) = (f g)(x) H(x) = 1 (3x - 4)-
Velshi Printers has contracts to complete weekly supplements required by fortysix customers. For the year 2018, manufacturing overhead cost estimates total $600,000 for an annual production capacity...
Find bases for each of the four fundamental subspaces of 3297 1181 2246 1215 1123
Find the orthogonal decomposition of With respect to 1012 W span
(a) Apply the Gram-Schmidt Process to to find an orthogonal basis for W = span{x1, x2, x3}. (b) Use the result of part (a) to find a QR factorization of 0111 1110 0111 1110
On-campus corporate presentations: Sympathy for the Devil Many students complain about the high number of corporate presentations taking place both on- and off-campus. In this question, we seek to...
How do organizations cultivate a culture of open innovation, leveraging crowdsourcing platforms, collaborative networks, and cross-industry partnerships to harness external knowledge and drive...
Braeden Sim is the accountant for Sim's Internet Service. From the following information, his task is to construct a balance sheet as of April 30, 201X, in proper form. Could you help him? (Click the...

(a) Show that any set of four vectors in R2 is linearly dependent. (b) Is this true...

Question:

Step by Step Answer:

a For any a 11 a 24 yields a linear system a 11 c 1 a 12 c 2 a 13 c 3 a 14 c 4 0 a ...View the full answer

Linear Algebra

Students also viewed these Linear Algebra questions