# There are many others 23 ex 1324 in exercises 23 and

• Homework Help
• 14
• 79% (14) 11 out of 14 people found this document helpful

This preview shows page 7 - 9 out of 14 pages.

There are many others.
23.Ex. 1.3.24:In Exercises 23 and 24, mark each statement True or False. Justify each answer.a.Whenuandvare nonzero vectors,Span{u,v}contains only the line throughuand the origin, and the linethroughvand the origin.b.Any list of five real numbers is a vector inR5.c.Asking whether the linear system corresponding to an augmented matrixa1a2a3bhas a solution amountsto asking whetherbis inSpan{a1,a2,a3}.d.The vectorvresults when a vectoru-vis added to the vectorv.e.The weightsc1, . . . , cpin a linear combinationc1v1+· · ·+cpvpcannot all be zero.7
e.False. For example, the paragraph before the heading “A Geometric Description of Span{v}and Span{u,v}sets all ofc1, . . . , cpequal to zero. This is why0is always in Span{v1, . . . ,vp}.24.Ex. 1.3.26:LetA=206-1851-21, letb=1037, and letWbe the set of all linear combinations of the columnsofA.a.IsbinW?b.Show that the second column ofAis inW.Scratch work.According to the problem,Wjust means everything inR3that can be written as a linear combinationof the columns ofA. So asking ifbis inWis a roundabout way of asking ifbcan be written as a linear combinationof the columns ofA.b. Let the three columns ofAbea,a, anda. Becausea= 0a+ 1a+ 0a,ais a linear combination of the
12321232columns ofA, soa2is inW.Section 1.425.Ex. 1.4.2:Compute the products in Exercises 1–4 using(a)the definition, as in Example 1, and(b)the row-vectorrule for computingAx. If a product is undefined, explain why.

Course Hero member to access this document

Course Hero member to access this document

End of preview. Want to read all 14 pages?