Vector Spaces

  • Thread starter ECE
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  • #1
ECE
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Let u and v be (fixed) vectors in the vector space V. Show that the set W of all linear combinations au+bv of u and v is a subspace of V.

I cannot prove the above proof properly. Can anyone help.

-Thanks
 

Answers and Replies

  • #2
radou
Homework Helper
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Let u and v be (fixed) vectors in the vector space V. Show that the set W of all linear combinations au+bv of u and v is a subspace of V.

I cannot prove the above proof properly. Can anyone help.

-Thanks

Take two vectors from W, and show that their linear combination is also in W.
 
  • #3
HallsofIvy
Science Advisor
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"Take two vectors from W" means taking two linear combinations, perhaps with different "a" and "b', say au+ bv and cu+ dv. "Their linear combination" would be something like x(au+ bv)+ y(cu+ dv) for numbers, x and y. "Show it is also in W" means "show it satisfies the definition of W". Here that means show that it also can be written au+ bv for some choices of a and b.
 
  • #4
ECE
7
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Thanks i understand it now
 

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