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Show: Vectors e.g.(a,b,1) do not form vector space.

  • #1
890
38

Homework Statement


upload_2018-8-12_19-29-5.png


Homework Equations


definition of null vector,
upload_2018-8-12_19-40-16.png
[/B]

The Attempt at a Solution


null vector : ## |0 \rangle = (0,0,0) ##
inverse of (a,b,c) = ( - a, -b, -c)
vector sum of the two vectors of the same form e.g. (c,d,1) + ( e,f,1) = ( c+e, d+f, 2) does not have the same form. So, the vectors of the form ( a,b,1) do not form a vector space.

Is this correct?
 

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Answers and Replies

  • #2
12,652
9,172
Yes, or even easier ##(0,0,0) \notin \{\,(a,b,1)\,\}##.
 
  • #3
890
38
Yes, or even easier ##(0,0,0) \notin \{\,(a,b,1)\,\}##.
Thanks for it.
 

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