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Consider the set V of all vectors of the form (x y 2) where x, y and z are real numbers 3. Show that Vis a vector space. 4. Is it true that each vector (x y z) from the vector space V can be written as the linear com bination x e1+ y ea+ zer of the unit vectors e1, ez and e?

Consider the set V of all vectors of the form (x y 2) where x, y and z are real numbers 3. Show that Vis a vector space. 4. Is it true that each vector (x y z) from the vector space V can be written as the linear com bination x e1+ y ea+ zer of the unit vectors e1, ez and e?

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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Consider the set V of all vectors of the form (x y 2) where x, y and z are real numbers 3. Show that Vis a vector space. 4. Is it true that each vector (x y z) from the vector space V can be written as the linear combination x e1+ y e+zez of the unit vectors e, ezand e?
Transcribed Image Text:Consider the set V of all vectors of the form (x y 2) where x, y and z are real numbers 3. Show that Vis a vector space. 4. Is it true that each vector (x y z) from the vector space V can be written as the linear combination x e1+ y e+zez of the unit vectors e, ezand e?
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