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Chapter 6 Solutions
Linear Algebra with Applications (2-Download)
- Find a basis for R2 that includes the vector (2,2).arrow_forwardConsider 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_forwardProve that in a given vector space V, the zero vector is unique.arrow_forward
- Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that among all the scalar multiples cv of the vector v, the projection of u onto v is the closest to u that is, show that d(u,projvu) is a minimum.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_forwardIllustrate properties 110 of Theorem 4.2 for u=(2,1,3,6), v=(1,4,0,1), w=(3,0,2,0), c=5, and d=2. THEOREM 4.2Properties of Vector Addition and Scalar Multiplication in Rn. Let u,v, and w be vectors in Rn, and let c and d be scalars. 1. u+v is vector in Rn. Closure under addition 2. u+v=v+u Commutative property of addition 3. (u+v)+w=u+(v+w) Associative property of addition 4. u+0=u Additive identity property 5. u+(u)=0 Additive inverse property 6. cu is a vector in Rn. Closure under scalar multiplication 7. c(u+v)=cu+cv Distributive property 8. (c+d)u=cu+du Distributive property 9. c(du)=(cd)u Associative property of multiplication 10. 1(u)=u Multiplicative identity propertyarrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
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