Subspaces: plane of vectors, linear combinations, vectors w/

[svalik]

Need a little help figuring whether the following subsets are actually subspaces:

1. the plane of vectors (b1, b2, b3) with b1=b2
2. the plane of vectors with b1 = 1
3. all linear combinations of v=(1,4,0) and w=(2,2,2)
4. all vectors that satisfy b1+b2+b3 = 0
5. all vectors with b1<= b2 <= b3

i'm having difficulties figuring which one satisfy the subspace requirements and how exactly the prove it... please help!!!

 

[stapel]

i'm having difficulties figuring which one satisfy the subspace requirements and how exactly the prove it...

Hint: Look at the subspace requirements involving zero. They're often helpful in quickly eliminating sets which are not subspaces. (For those that are, you simply have to go through the list and display that generic elements from the set will indeed obey the rules.) :wink:

Eliz.