Subspaces; Linear span

  • Thread starter dracolnyte
  • Start date
  • #1
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Homework Statement


(i)Show that the linear span of the vector a1 = (-7, 8, 5) is the line whose equation is
x/(-7) = y/8 = z/5

The Attempt at a Solution


The problem is, I don't know where or how to start.
 

Answers and Replies

  • #2
Dick
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Define the 'linear span of a vector'. Look it up if you have to.
 
  • #3
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The linear span of a vector is the collection of all linear combinations of the vectors a1, a2..., ak
 
  • #4
Dick
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Ok, so for one vector v1 it's the set of all vectors k*v1 for k any real number, right?
 
  • #5
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Ya, and then?
 
  • #6
Dick
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You are supposed to be helping here. Guess. (x,y,z) is a point in the span of (-7, 8, 5). What's it equal to?
 
  • #7
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Okay so
-7k = x
8k = y
5k = z
 
  • #8
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Got it, thank you so much. I'll be back with more for sure lol.
 

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