SOLUTION: Find a basis of R^4 which contains the vectors (1,1,1,1) and (1,2,3,4). I know how to show a set of vectors is in the basis, but I'm having trouble working this one backwards and

Algebra ->  Algebra  -> College  -> Linear Algebra -> SOLUTION: Find a basis of R^4 which contains the vectors (1,1,1,1) and (1,2,3,4). I know how to show a set of vectors is in the basis, but I'm having trouble working this one backwards and       Log On


   

Question 22335: Find a basis of R^4 which contains the vectors (1,1,1,1) and (1,2,3,4). I know how to show a set of vectors is in the basis, but I'm having trouble working this one backwards and finding a basis for the set of vectors.
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Find a basis of R^4 which contains the vectors (1,1,1,1) and (1,2,3,4).
Note the dim of R%5E4+ is 4, now you already have two indep.vectors,
just try to find another 2 indep. vectors(from them) to form a basis.
There are infinite many such vectors, say choose (1,0,0,0),(0,1,0,0).
Then check the 4 vectors are indep.
Kenny