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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+1 a - 4b 2b +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 the zero vector is not in W. 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 not all vectors u in W have the property 1u = u.

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+1 a - 4b 2b +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 the zero vector is not in W. 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 not all vectors u in W have the property 1u = u.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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+1 a - 4b 2b +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.) B. The set W is not a vector space because the zero vector is not in W. 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 not all vectors u in W have the property 1u = u.
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+1 a - 4b 2b +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.) B. The set W is not a vector space because the zero vector is not in W. 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 not all vectors u in W have the property 1u = u.
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