Is Row Reduction Enough to Prove a Subset of Vectors?

[transgalactic]

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?

 

[buffordboy23]

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?

 

[transgalactic]

http://img408.imageshack.us/img408/2364/89390838kq8.gif

 

[transgalactic]

this last part is row reduction question..

i don't know how to build the build matrix

 

[HallsofIvy]

What set is it that you are trying to prove is a subspace?

 

[transgalactic]

i am trying to prove that u(k1) is a subset of v(k2)

 

[transgalactic]

how to solve the second part?

 

[buffordboy23]

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.