Show that every basis for R n must contain exactly n vectors. Let S = {v 1
Question:
Show that every basis for Rn must contain exactly n vectors.
Let S = {v1,...,vk} be a set of k vectors in Rn, with k n.
Data from in Theorem
Transcribed Image Text:
If a set S = {₁,..., Vps in R" contains the zero vector, then the set is linearly dependent. PROOF By renumbering the vectors, we may suppose v₁ = 0. Then the equation 1v₁ + 0v₂ + + Ovp = 0 shows that S is linearly dependent.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (1 review)
Let A be the n k matrix v 1 v k Since A has fewer columns than rows there cannot be a ...View the full answer
Answered By
Issa Shikuku
I have vast experience of four years in academic and content writing with quality understanding of APA, MLA, Harvard and Chicago formats. I am a dedicated tutor willing to hep prepare outlines, drafts or find sources in every way possible. I strive to make sure my clients follow assignment instructions and meet the rubric criteria by undertaking extensive research to develop perfect drafts and outlines. I do this by ensuring that i am always punctual and deliver quality work.
5.00+
6+ Reviews
13+ Question Solved
Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
Question Posted:
Students also viewed these Mathematics questions
-
Show that every basis for R n must contain exactly n vectors. Let S = {v 1 ,...,v k } be a set of k vectors in R n , with k > n. Use a theorem from Chapter 1 to explain why S cannot be a basis for R...
-
Let {u1, . . . , um} be a set of vectors in an n-dimensional vector space V and let B be a basis for V. Let S = {[u1]B , . . . , [um] B} be the set of coordinate vectors of {u1, . . . , um} with...
-
Let {v1, . . . , vn} be a set of orthonormal nonzero vectors in Rn and x Rn. Determine the values of ck, for k = 1, 2, . . . , n, if CE
-
On 1 January 2022, ABC Company issued 10,000 shares of common stock for $100,000. On 31 December 2022, the company declared and paid dividends of $10,000. Calculate the earnings per share and the...
-
Crandon Company acquires an ore mine at a cost of $6,300,000. It incurs additional costs of $500,000 to access the mine, which is estimated to hold 1,000,000 tons of ore. The estimated value of the...
-
A piece of glass with a flat surface is at the bottom of a tank of water. If a ray of light traveling in the glass is incident on the interface with the water at an angle with respect to the normal...
-
Teddy Sargent opened an accounting firm on May 1, 2010. During the month of May, the business completed the following transactions: Requirements 1. Open, or set up, the following T-accounts: Cash,...
-
The Citrix Fund has invested in a portfolio of government bonds that has a current market value of $44.8 million. The duration of this portfolio of bonds is 13.5 years. The fund has borrowed to...
-
The Twain Mill Company has issued rights to its shareholders.The stock is currently selling for $20 rights-on.The subscription price on the rights offering is $18.Three rights are required to...
-
In your opinion, what is the main benefit of wise financial planning?
-
Concern the crystal lattice for titanium, which has the hexagonal structure shown on the left in the accompanying figure. The vectors in R 3 form a basis for the unit cell shown on the right. The...
-
It can be shown that a solution of the system below is x 1 = 3, x 2 = 2, and x 3 = -1. Use this fact and the theory from this section to explain why another solution is x 1 = 30, x 2 = 20, and x 3 =...
-
Refer to the information provided in E12.17, but now assume that Lighting Designs Corp. is a publicly accountable company. At December 31, 2020, the copyrights value in use is $1,850,000 and its...
-
The following physicochemical catalyst properties are to be determined: Surface complexes Number and type of active centers Specific surface area and pore radius distribution A) B) C) D) Element...
-
A 0.25kg cart travelling at 3.0 m/s collides with and sticks to a .125 moving with an unknown speed and direction on a level track. They move off together and stop at a vertical height of .142m What...
-
Tara Palmer Tomkinson and the It Girls Tara Palmer Tomkinson has become one of the most well-known British celebrities over the last ten years. At the age of 20, she was photographed for Tatler...
-
Luzadis Company makes furniture using the latest automated technology. The company uses a job-order costing system and applies manufacturing overhead cost to products based on machine-hours. The...
-
97. Arrange the following carbanions in decreasing order of stability :- e CH CH CH2 CH2 CH3 NO OCH3 (I) (II) (III) (IV) (1) III>I>IV> II (2) III>II>I>IV (3) I> III>II>IV (4) III>I>II>IV
-
A process at a manufacturing plant produces a two-layer film. Each layer thickness is measured by a properly calibrated measuring device. The first layer has a target mean specification of 0.055 in....
-
Jax Incorporated reports the following data for its only product. The company had no beginning finished goods inventory and it uses absorption costing. $ 57.30 per unit $ 10.30 per unit $ 7.80 per...
-
Refer to Exercises 9.99.11. What do the probabilities tell you about the variances of X and X?
-
Use the F table (Table 6) to find the following values of F. a. F. 025, 8, 22 b. F .05, 20, 30 c. F .01, 9, 18 d. F .025, 24, 10
-
Use the F table (Table 6) to find the following values of F. a. F .05, 3, 7 b. F .05, 7, 3 c. F .025, 5, 20 d. F .01, 12, 60
-
Question Using latest set of the published accounts Analyze at least 3 parent companies listed at the Lusaka securities exchange ( LuSE . ) Outline the group structure and determine which ones are...
-
Frustrated by high property tax rates, resident in the Village of Williamsville voted to dissolve their village government, instead agreeing to receive similar services (formerly provided by the...
-
Use the One - Shot Model to calculate the Firm's Bankruptcy Cost: Probability of Bankruptcy: 2 7 % Fraction of the firm lost in the bankruptcy: 3 0 % Value of the unlevered firm: 1 0 0 , 0 0 0 Value...
Study smarter with the SolutionInn App