Consider the set of all ordered lists of three complex numbers: (ax,ay,az). This forms a vector space. What if you constrained the set to those where ax = ay = az. Does this still constitute a vector space? If it does, explicitly show that it satisfies all eight properties required of a vector space. If not, which property fails? Show how it fails.
Consider the set of all ordered lists of three complex numbers: (ax,ay,az). This forms a vector space. What if you constrained the set to those where ax = ay = az. Does this still constitute a vector space? If it does, explicitly show that it satisfies all eight properties required of a vector space. If not, which property fails? Show how it fails.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the set of all ordered lists of three complex numbers: (ax,ay,az). This forms a vector space. What if you constrained the set to those where ax = ay = az. Does this still constitute a vector space? If it does, explicitly show that it satisfies all eight properties required of a vector space. If not, which property fails? Show how it fails.
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VIEWStep 3: Associativity and Commutativity of Addition
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