Please answer question completely and give correct answers thanks Let {u1, u2, U3, u4} be a linearly dependent set of vectors.Select the best statement.O A. {u1, U2, Uz} is always a linearly dependent set of vectors.O B. {u1, U2, U3} is a linearly dependent set of vectors unless one of {u1, u2, U3} is the zero vector.OC. {u1, U2, Uz} could be a linearly dependent or linearly dependent set of vectors depending on the vector space chosen.O D. {u1, u2, U3} could be a linearly dependent or linearly dependent set of vectors dependingO E. {u1, u2, U3} is never a linearly dependent set of vectors.on the vectors chosen.OF none of the above

Let {U1, U2, U3, U4} be a linearly dependent set of vectors "When at least one of the vectors from a…

Let {u1, u2, U3, u4} be a linearly dependent set of vectors. Select the best statement. O A. {u1, U2, Uz} is always a linearly dependent set of vectors. O B. {u1, U2, Us} is a linearly dependent set of vectors unless one of{u1, U2, U3} is the zero vector. OC. {u1, U2, U3} could be a linearly dependent or linearly dependent set of vectors depending O D. {u1, u2, U3} could be a linearly dependent or linearly dependent set of vectors depending on the vector space chosen. on the vectors chosen.

Let {u1, u2, U3, u4} be a linearly dependent set of vectors. Select the best statement. O A. {u1, U2, Uz} is always a linearly dependent set of vectors. O B. {u1, U2, Us} is a linearly dependent set of vectors unless one of{u1, U2, U3} is the zero vector. OC. {u1, U2, U3} could be a linearly dependent or linearly dependent set of vectors depending O D. {u1, u2, U3} could be a linearly dependent or linearly dependent set of vectors depending on the vector space chosen. on the vectors chosen.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 21EQ

See similar textbooks

Similar questions

Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set {v12v2,2v23v3,3v3v1} linearly dependent or linearly independent? Explain.
Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check your work against the answers in the back of the book. Write w=(7,2,4) as a linear combination of the vectors v1, v2 and v3 if possible. v1=(2,1,0), v2=(1,1,0), v3=(0,0,6)
Proof When the set of vectors {u1,u2,...,un} is linearly independent and the set {u1,u2,...,un,v} is linearly dependent, prove that v is the linear combination of the uis.
Determine whether the vectors u=6,10 and v=5,3 are orthogonal.
Proof When V is spanned by {v1,v2,...,vk} and one of these vector can be written as a linear combination of the other k1 vectors, prove that the span of these k1 vector is also V.
Mark each of the following statements true or false: Forvectorsu,v,andwinn,ifu+w=v+wthenu=v. Forvectorsu,v,andwinn,ifuw=vw,thenu=v Forvectorsu,v,andwin3,ifuisorthogonaltov,andvisorthogonaltow,thenuisorthogonaltow. In3,ifalinelisparalleltoaplaneP,thenadi-rectionvectordforlisparalleltoanormalvectornforP. In3,ifalinelisperpendiculartoaplaneP,thenadirectionvectordforlisaparalleltoanormalvectornforP. 3,iftwoplanesarenotparallel,thentheymustintersectinaline. In3,iftwolinesarenotparallel,thentheymustintersectinapoint. Ifvisabinaryvectorsuchthatvv=0,thenv=0. In5,ifab=0theneithera=0orb=0. ln6,ifab=0theneithera=0orb=0
Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {vu,wv,uw} is linearly independent or linearly dependent.
Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)