Is Row Reduction Enough to Prove a Subset of Vectors?

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transgalactic
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i know that in order to prove that one group of vectors are a part of another
i need to stack them up

i did row reduction and i don't know how to extract a vector for the group

http://img384.imageshack.us/img384/2546/55339538nk4.gif

this came from this question part 2

http://img116.imageshack.us/img116/1152/25587465vv2.gif

in the U group i have equations with "k"
i don't know what vectors to take?
 
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Have you tried using orthogonality? If the vectors span R^(3), then they must be linearly independent; how can you show that two vectors are perpendicular?
 
http://img408.imageshack.us/img408/2364/89390838kq8.gif
 
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this last part is row reduction question..

i don't know how to build the build matrix
 
i am trying to prove that u(k1) is a subset of v(k2)
 
What does it mean for one set (call it A) to be a subset of another (call it B)? Every element in A must be an element in B. You must show that every element satisfies this requirement, or else it isn't a subset.