Question

Use the proof of the contraction theorem as a recipe for finding a subset of

{(0,2,1,-2),(1,1,1,0),(-1,1,0,2),(1,-1,0,2)}

that is a basis for the subspace of R4 spanned by this set.

Answer 1

the first 3 vectors form a basis...just make a matrix and row reduce it.

Answer 2

this is the matrix i ended with. \[\left[\begin{matrix}0 & 1& -1 & 1 \\ 1 & 1 & 0 & 0 \\ 0 & 0 & 0 &0 \\ 0 & 0 & 0 &0\ \end{matrix}\right]\]

Answer 3

is that right or wrong? and if its right, how do i read it correctly to determine which ones used as my basis. I originally said, {(0,2,1,-2), (-1,1,0,2)}

Answer 4

that matrix is not in ref