Let u be a linear combination of {1₁, 1₂, 13).Select the best statement.OA. {U₁, U₂, U3, U4} is a linearly dependent set of vectors unless one of {1₁, 12, 13} is the zero vector.OB. (U₁, U₂, U3, U4} is always a linearly dependent set of vectors.OC. {U₁, U₂, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vectors chosen.OD. {U₁, U₂, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vector space chosen.OE. {U₁, U₂, U3, U4} is never a linearly dependent set of vectors.OF. none of the above

Answered: Image /qna-images/answer/19b91ae9-59ef-4b97-adf3-0bdc99316832.jpg

Answered: Select the best statement.

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

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
Determine whether the vectors u=6,10 and v=5,3 are orthogonal.
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 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.
For each of the following pairs of points, draw the vector AB. Then compute and redraw AB as a vector in standard position. (a)A=(1,1),B=(4,2)(b)A=(0,2),B=(2,1)(c)A=(2,32),B=(12,3)(d)A=(13,13),B=(16,12)

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781337278461

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS