For A as in Exercise 12, find a nonzero vector in Nul A and a nonzero vector in Col A.
12. A =
Trending nowThis is a popular solution!
Chapter 2 Solutions
Linear Algebra and Its Applications (5th Edition)
Additional Math Textbook Solutions
Elementary Statistics: Picturing the World (7th Edition)
Mathematics for the Trades: A Guided Approach (11th Edition) (What's New in Trade Math)
Math in Our World
College Algebra (Collegiate Math)
Elementary Statistics
Thinking Mathematically (6th Edition)
- Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of its length. b u has the direction opposite that of v and twice its length.arrow_forwardLet 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.arrow_forwardFind a unit vector u in the direction of v=i+jarrow_forward
- 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)arrow_forwardMark 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=0arrow_forwardIn Exercises 13 and 14, give the vector equation of the plane passing through , and . 13.arrow_forward
- 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.arrow_forwardFind a basis for R2 that includes the vector (2,2).arrow_forwardIn vector form as in Exercises 5 and 6, find an equation for the line through the point 4,1,-3 and with the direction vector 1,2,3.arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,