subspace

[hkus10]

1) Let x0 be a fixed vector in a vector space V. Show that the set W consisting of all scalar multiples cx0 of x0 is a subspace of V.

 

What techniques should I use to prove this?

 

2a) Show that a line lo through the origin of R^n is a subspace of R^n.

2b) show that a line l in R^n not passing through the origin is not a subspace of R^n.

 

What techniques and direction should I use to solve these problems?

 

Thanks

Edited March 9, 2011 by swansont
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[DrRocket]

1) Let x0 be a fixed vector in a vector space V. Show that the set W consisting of all scalar multiples cx0 of x0 is a subspace of V.

 

What techniques should I use to prove this?

 

2a) Show that a line lo through the origin of R^n is a subspace of R^n.

2b) show that a line l in R^n not passing through the origin is not a subspace of R^n.

 

What techniques and direction should I use to solve these problems?

 

Thanks

 

 

If it were me I would choose a technique that addressed the given problem.

Edited March 9, 2011 by swansont
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[ajb]

What techniques should I use to prove this?

 

Ask yourself some questions:

 

1. What is a vector space?
   
2. What is a subspace of a vector space?
   

 

Get it clear in your mind what these are. Then see if the data given in the questions if sufficient to decide if you have subspaces or not. By "force" see if the axioms for subspaces hold.