Question: Let S1 = {u1, u2, ..., um} and S2 = {w1, w2, ..., wn} be two subsets of a vector space V that are disjoint

Let S1 = {u1, u2, ..., um} and S2 = {w1, w2, ..., wn} be two subsets of a vector space V that are disjoint (so no ui is equal to any wj ) with S1 linearly independent and S2 linearly independent. Suppose there exists v 6= 0 with v Span S1 and v Span S2. Is S1 S2 linearly dependent or independent? Prove your assertion is correct

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

4 This assignment, based on the content of Unit 4 of the Study Guide, is worth 3% of your grade. We recommend that you hand it in after you complete Unit 4. You must show all of your work in order to...

Give Correct ANSWERS Human-Computer Interaction (a) If you had been one of the original inventors of the WIMP interface, and engineers on the technical team had been sceptical about the advantages...

7. (a) Suppose S = {u1, u2, ..., uk} is an orthogonal basis for a subspace V of Rn. Let S' = U1 U2 uk will'1221'' be an orthonormal basis of V obtained from normalizing S. If the coordinate vector of...

Let B = {u1, u2, u3} be a basis for a vector space V, and let T: V V be a linear operator such that Find [T]B², where B² = {v1, v2, v3}, is the basis for V defined by v1 = u1, v2 = u1 + u2,...

15. (10 pts) 1. Let V = R2, and define addition and scalar multiplication as follows: utv = (u1, U2) + (U1, U2) = (u101, u202) ku = k(u1, u2) = (up, u) Given that V is a vector space, (a) determine...

Vi . uj Let S = {u1, u2, u3} and T = {V1, V2, V3} be two orthonormal bases for a subspace W. Let P = (p1 p2 P3), where pi = Vi . U2 for i = Vi . U3 1, 2, 3. Which of the following statement is true?...

Theorem 2.10. Let V be a vector space. Let T, U1, U2 E C(V). Then (a T(U1 + U2) = TU1 + TU2 and (U1 + U2) T = UIT + U2 T (b) T(U1 U2) = (TU1) U2 (C) TI = IT = T (d) a(U1U2) = (aU1)U2 = U1(aU2) for...

Can you help me with question 2 a and b 2. (a) Let U = {AE M2(R) : tr (A) = 0} be a subspace of M2(R), where tr (A) de trace of A. (i) Show that (ii) Find a basis for U. Justify your answer. (iii)...

Below figure shows a part of the production line of raspberry juice in F&B company. Initially, the production begins with the screw pressing of raspberies and topping of water to form the diluted...

You are the director of health information services at a large acute care hospital. The Risk Management Director is asking for your participation in their next risk assessment. 1. Identify an...

What is a key characteristic that distinguishes angel investors from venture capital firms? 1 Point Angel investors often have specialized expertise in the industry they invest in Angel investors...

A company issues 1,050 shares of its common stock for $33,600 cash. Prepare journal entries to record this event under each of the following separate situations.