Let S = (v1, v2, ( ( (( vn) be an ordered basis for the n-dimensional vector

Question:

Let S = (v1, v2, ( ( (( vn) be an ordered basis for the n-dimensional vector space V, and let v and w be two vectors in V. Show that v = w if and only if [v]S = [w]S.

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

Step by Step Answer:

Related Book For book-img-for-question

Elementary Linear Algebra with Applications

ISBN: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

See More Books

Question Posted: Jun 21, 2016 07:06 AM

See More Questions

Let S = (v1, v2, ( ( ( ( vk} be a basis for a subspace V of Rn that is obtained by the method of Example 1. If Belongs to V and the leading 1's in the reduced row echelon form from the method in...
Let S = (v1, v2, v3) be a set of nonzero vectors in R3 such that any two vectors in 5 are orthogonal. Prove that S is linearly independent.
Let S = {v1, v2,..., vk} be an orthonormal basis for the Euclidean space V and {a1, a2,..., ak) be any set of scalars none of which is zero. Prove that T = {a1v1,a2v2, ...,akvk} is an orthogonal...
On January 26, Nova Co. borrowed cash from Conrad Bank by issuing a 30-day note with a face amount of $60,000. Assume a 360-day year. a. Determine the proceeds of the note, assuming the note carries...
SunNet is a residential Internet Service Provider (ISP) in the central Florida area. Presently, the company operates one centralized facility that all of its clients call into for Internet access. To...
When should you define a separate function for part of a program? List reasons.
What are the modifications necessary for using HRIS software applications that are designed for domestic companies in an MNE?
In Fig two isotropic point sources S1 and S2 emit identical light waves in phase at wavelength . The sources lie at separation d on an x axis, and a light detector is moved in a circle of large...
The first image of ECG shows the heart rate at about 70 beats per second. For the sake of simplicity, for this case, assume 60 beats per minute. Also, for simplicity, assume that the patient has only...
The number of telephone calls arriving at an exchange during any given minute between noon and 1:00 P.M. on a weekday is a random variable with the following probability distribution. XP(x) 0 ....0.3...
Let V be the subspace of the vector space of all real-valued continuous functions that has basis S = {et, e-t}. Show that V and R2 are isomorphic.
Show that if S is an ordered basis for an n-dimensional vector space V, v and w are vectors in V, and c is a scalar, then And [v+w], = [v]s+[w],
What other steps can management take to be responsive to potential whistle-blowing situations?
The regulation of reproduction has been a a controversial topic for many years following the 1973 decision in Roe v Wade. The recent decision in Dobbs vs Jackson Women's Health Organization by the...
Jen tells her professor Dan that if he performs his torts rap in class a second time that she would give him a perfect rating at the end of the final exam. Dan then puts on a show complete with...
X and Y decide to incorporate a Singapore company to acquire a prime piece of real estate to build a block of flats consisting of 20 separate housing units. Both X and Y are directors and...
Healthcare systems are huge, complex, and constantly changing as they respond to economic, technological, social, and historical factors. The availability of technology has a profound effect on the...
Pacific Marine, Inc. is a boat retailer. Pacific contracts to sell a 20-foot sailboat to Fred Jones for $25,000. However, Fred repudiates before he is to take delivery. Pacific promptly resells the...
Kryll Company set the following standard costs per unit for its single product. Overhead is applied using direct labor hours. The standard overhead rate is based on a predicted activity level of 80%...
According to a recent survey, 40% of millennials (those born in the 1980s or 1990s) view themselves more as spenders than savers. The survey also reveals that 75% of millennials view social...
Dillon plans to invest $7500, part at 4% simple interest and the rest at 5% simple interest. What is the most that he can invest at 4% and still be guaranteed at least $325 in interest per year?
A university invests $600,000 at simple interest, part at 6%, half that amount at 4.5%, and the rest at 3.5%. What is the most that the university can invest at 3.5% and be guaranteed $24,600 in...
A foundation invests $50,000 at simple interest, part at 7%, twice that amount at 4%, and the rest at 5.5%. What is the most that the foundation can invest at 4% and be guaranteed $2660 in interest...
A taxpayer disposed a part of asset for 100,000 SR in cash. The taxpayer purchased that asset for 90,000 SR 5 years ago but the market value of the complete assets was as follows: Part disposed...
A company maintains debt/equity ratio of 0.6. The flotation cost of equity is 12% and flotation cost of debt it is 6%. The firm is considering a new project which will require $5 million in external...
Flight Caf prepares in-flight meals for airlines in its kitchen located next to a local airport. The company's planning budget for July appears below: Flight Caf Planning Budget For the Month Ended...

Let S = (v1, v2, ( ( (( vn) be an ordered basis for the n-dimensional vector

Question:

Step by Step Answer:

Let v w The coordinates of a vector relative to basis S are the coeffici...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions