Prove that if U and W are both three-dimensional subspaces of R5 then U W is

Question:

Prove that if U and W are both three-dimensional subspaces of R5 then U ∩ W is non-trivial. Generalize.

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 01:55 AM

See More Questions

Prove that if u and v are vectors in a complex inner product space, then 4 4 4
Let V be an inner product space. Prove that if u and v are any vectors in V, then ||u + v||2 = ||u||2 + ||v||2 if and only if (u, v) = 0, that is, if and only if u and v are orthogonal. This result...
Suppose that V is open in R2, that H = [a, b] [0, c] V, that : V R is C2 on V, and that (x0, t0) > 0 for all (x0, t0) H. a) Show that, given > 0, there is a compact set K such that u(x, t) > -...
With respect to strategies used by land conservation groups to preserve land, conservation easements seem to be expanding more rapidly than buying land for preservation. In what respect might...
What is resale price maintenance, and why is it controversial?
Determine the moments at the supports, then draw the moment diagram. Assume B is a roller and A and Care fixed. EI is constant. 15 kN 15 kN 15 kN 25 kN/m TB +2 m--2 m--2 m--2 m- A 3m- -6 m.
Meddevco (name changed) is a large multinational corporation that operates in the medical devices sector. The firm employs around 33,000 people in five divisions and has operations in 120 countries....
Ida, who has AGI of $80,000 before considering rental activities, is active in three separate real estate rental activities. Ida has a marginal tax rate of 28%. She has $12,000 of losses from...
Bramble Corp, applies overhead on the basis of machine hours. Given the following data, what is the amount of overhead applied and the amount by which it is under- or overapplied for the period?...
Your sister has just won $300,000 (taxfree) in the state lottery. Shes decided to quit her job and devote herself to writing novels for the next ten years, using her lottery winnings to support...
Where is a basis, show that in this equation each of the c i s is zero. Generalize. (B1,..., Bn)
Theorem 1.12 shows that, with respect to a basis, every linear combination is unique. If a subset is not a basis, can linear combinations be not unique? If so, must they be?
Suppose short-run inverse demand in a monopolistically competitive market is represented by: p(x) = 18 - 0.2x. Cost is given by: TC(x) = 320 + 2x + 0.05x2. a. (liven these demand and cost conditions,...
Your project sponsor informed you that you have to deliver your project much sooner than anticipated. When you break the news to your team, they are not happy with the decision; they are concerned...
Users will often describe their objectives in qualitative language. The project manager must work with the user to provide quantifiable definitions to those qualitative terms. These quantifiable...
Watch the assigned movie Gung Ho 1986 and discuss the impact of culture on the different forms of leadership approaches throughout the movie and if the cultural behaviors are either learned,...
Consider an orthopedist's office all arriving patients first check in at a reception area where they fill out the necessary paperwork. On average, it takes 10 minutes to complete check-in and there...
Explain the transaction that took place that resulted in the documents below. Who can complete each of the above transactions? WORLD BANK Banking Corporation Wedgewood NSW Date 15 May 20XX Payee...
For the following exercises, evaluate or solve, assuming that the function f is one-to-one. If f(3) = 2, find f 1 (2).
When an electric field is applied to a shallow bath of vegetable oil, why do tiny bits of thread floating in the oil align with the field like compasses in a magnetic field?
Show that there is no linear transformation T: R3 P2 such that 0 6 2 + 2x2
Let {v1, . . . , vn} be a basis for a vector space V and let T: V V be a linear transformation. Prove that if T (v1) = V1, T (v2) = V2 . . . , T(vn) = vn, then T is the identity transformation on V.
Let T: Pn Pn be a linear transformation such that T(xk) = kxk-1 for k = 0, 1 , . . . , n. Show that T must be the differential operator D.
How do I view vector and bitmap images in a VR headset?
The radius of a solid conducting sphere is R = 14.0 cm and it has a uniformly distributed charge of 30.5 nC on its surface. The center of the sphere is at the origin of the xy coordinate system. The...
What is the best file format for digital images, such as photos and scans?

Prove that if U and W are both three-dimensional subspaces of R5 then U W is

Question:

Step by Step Answer:

Let BU be a basis for U and let BW be a basis for W ...View the full answer

Linear Algebra

Students also viewed these Linear Algebra questions