Let W be the set of all vectors of the form shown on the right, where a and b represent arbitrary real numbers. Find a set S of vectors that spans W, or give an example or an explanation showing why W is not a vector space. -a +5 a-3b 5b + a Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The set W is a vector space and a spanning set is S= (Use a comma to separate vectors as needed.) OB. The set W is not a vector space because not all vectors u in W have the property 1u= u. O C. The set W is not a vector space because not all vectors u, v, and w in W have the property that u+v=v+u and (u+v)+w=u+(v+w). O D. The set W is not a vector space because the zero vector is not in W.

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let W be the set of all vectors of the form shown on the right, where a and b
represent arbitrary real numbers. Find a set S of vectors that spans W, or give an
example or an explanation showing why W is not a vector space.
-a +5
a-3b
5b + a
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The set W is a vector space and a spanning set is S=
(Use a comma to separate vectors as needed.)
O B.
The set W is not a vector space because not all vectors u in W have the property 1u= u.
O C.
The set W is not a vector space because not all vectors u, v, and w in W have the property that u + v=v+u
and (u + v) +w=u+(v +w).
O D. The set W is not a vector space because the zero vector is not in W.
Transcribed Image Text:Let W be the set of all vectors of the form shown on the right, where a and b represent arbitrary real numbers. Find a set S of vectors that spans W, or give an example or an explanation showing why W is not a vector space. -a +5 a-3b 5b + a Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The set W is a vector space and a spanning set is S= (Use a comma to separate vectors as needed.) O B. The set W is not a vector space because not all vectors u in W have the property 1u= u. O C. The set W is not a vector space because not all vectors u, v, and w in W have the property that u + v=v+u and (u + v) +w=u+(v +w). O D. The set W is not a vector space because the zero vector is not in W.
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