The problem involves determining a basis for a subspace V spanned by a given set of vectors in a vector space context.
Some participants have provided guidance on the relationship between linear independence and the determination of a basis, noting that if the vectors are linearly independent, they form a basis, while a subset would form a basis if they are dependent. Multiple interpretations of the vectors' arrangement are being explored.
There is a lack of clarity on the arrangement of the vectors as row or column vectors, which may influence the approach to the problem.
dmitriylm said:Homework Statement
Let V be the subspace spanned by the following vectors:
[ 0]...[ 1 ]...[2]
[ 2]...[ 1 ]...[5]
[-1]...[3/4]...[0]
Determine a basis for V.
The Attempt at a Solution
I'm not quite sure how to start here. Would placing the vectors in a matrix and deriving its reduced echelon form give me a basis?
Mark44 said:Are these row vectors or column vectors?